var bibbase_data = {"data":"<img src=\"//bibbase.org/img/ajax-loader.gif\" id=\"spinner\"\n  style=\"display: none;\" alt=\"Loading..\" />\n\n<div id=\"bibbase\">\n\n  <script type=\"text/javascript\">\n    var bibbase = {\n      params: {\"bib\":\"https://bingtan.me/scopus.bib\",\"jsonp\":\"1\",\"group0\":\"year\",\"groupby\":\"author_short\",\"folding\":\"1\",\"nocache\":\"1\",\"authorFirst\":\"1\",\"noTitleLinks\":\"true\",\"theme\":\"default\",\"showSearch\":\"1\",\"host\":\"bibbase.org\"},\n      data: [{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Qin\"],\"firstnames\":[\"Xiaolong\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Wang\"],\"firstnames\":[\"Xianfu\"],\"suffixes\":[]}],\"title\":\"Alternated inertial algorithms for split feasibility problems\",\"journal\":\"Numerical Algorithms\",\"year\":\"2024\",\"volume\":\"95\",\"number\":\"2\",\"pages\":\"773–812\",\"doi\":\"10.1007/s11075-023-01589-8\",\"url\":\"https://bingtan.me/files/paper/TQW-NUMA2024.pdf\",\"abstract\":\"We introduce four novel relaxed CQ algorithms with alternating inertial for solving split feasibility problems in real Hilbert spaces. The proposed algorithms employ a new non-monotonic adaptive step size criterion and utilize two different step sizes in each iteration. The weak convergence of the iterative sequences generated by the proposed algorithms is established under some weak conditions. Moreover, the Fejér monotonicity of the even subsequence with respect to the solution set is recovered. Two applications in signal denoising and image deblurring are given to illustrate the computational efficiency of our algorithms.\",\"keywords\":\"Split feasibility problem, CQ method, Projection and contraction method, Alternated inertial method, Signal processing, Image restoration\",\"abbrev_source_title\":\"Numer. Algorithms\",\"bibtex\":\"@ARTICLE{TQW_NUMA24,\\nauthor={Tan, Bing and Qin, Xiaolong and Wang, Xianfu},\\ntitle={Alternated inertial algorithms for split feasibility problems},\\njournal={Numerical Algorithms},\\nyear={2024},\\nvolume={95},\\nnumber={2},\\npages={773--812},\\ndoi={10.1007/s11075-023-01589-8},\\nurl={https://bingtan.me/files/paper/TQW-NUMA2024.pdf},\\nabstract={We introduce four novel relaxed CQ algorithms with alternating inertial for solving split feasibility problems in real Hilbert spaces. The proposed algorithms employ a new non-monotonic adaptive step size criterion and utilize two different step sizes in each iteration. The weak convergence of the iterative sequences generated by the proposed algorithms is established under some weak conditions. Moreover, the Fejér monotonicity of the even subsequence with respect to the solution set is recovered. Two applications in signal denoising and image deblurring are given to illustrate the computational efficiency of our algorithms.},\\nkeywords={Split feasibility problem,  CQ method,  Projection and contraction method,  Alternated inertial method,  Signal processing,  Image restoration},\\nabbrev_source_title={Numer. Algorithms},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Qin, X.\",\"Wang, X.\"],\"key\":\"TQW_NUMA24\",\"id\":\"TQW_NUMA24\",\"bibbaseid\":\"tan-qin-wang-alternatedinertialalgorithmsforsplitfeasibilityproblems-2024\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TQW-NUMA2024.pdf\"},\"keyword\":[\"Split feasibility problem\",\"CQ method\",\"Projection and contraction method\",\"Alternated inertial method\",\"Signal processing\",\"Image restoration\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Xie\"],\"firstnames\":[\"Zhongbing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Cai\"],\"firstnames\":[\"Gang\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]}],\"title\":\"Inertial subgradient extragradient method for solving pseudomonotone equilibrium probelms and fixed point problems in Hilbert spaces\",\"journal\":\"Optimization\",\"year\":\"2024\",\"volume\":\"73\",\"number\":\"5\",\"pages\":\"1329-1354\",\"doi\":\"10.1080/02331934.2022.2157677\",\"url\":\"https://bingtan.me/files/paper/XCT-OPT2024.pdf\",\"abstract\":\"This paper proposes a new inertial subgradient extragradient method for solving equilibrium problems with pseudomonotone and Lipschitz-type bifunctions and fixed point problems for nonexpansive mappings in real Hilbert spaces. Precisely, we prove that the sequence generated by proposed algorithm converges strongly to a common solution of equilibrium problems and fixed point problems. We use an effective self-adaptive step size rule to accelerate the convergence process of our proposed iterative algorithm. Moreover, some numerical results are given to show the effectiveness of the proposed algorithm. The results obtained in this paper extend and improve many recent ones in the literature.\",\"keywords\":\"Inertial method, Subgradient extragradient method, Equilibrium probelm, Fixed point problem, Strong convergence\",\"abbrev_source_title\":\"Optimization\",\"bibtex\":\"@ARTICLE{XCT_OPT24,\\nauthor={Xie, Zhongbing and Cai, Gang and Tan, Bing},\\ntitle={Inertial subgradient extragradient method for solving pseudomonotone equilibrium probelms and fixed point problems in Hilbert spaces},\\njournal={Optimization},\\nyear={2024},\\nvolume={73},\\nnumber={5},\\npages={1329-1354},\\ndoi={10.1080/02331934.2022.2157677},\\nurl={https://bingtan.me/files/paper/XCT-OPT2024.pdf},\\nabstract={This paper proposes a new inertial subgradient extragradient method for solving equilibrium problems with pseudomonotone and Lipschitz-type bifunctions and fixed point problems for nonexpansive mappings in real Hilbert spaces. Precisely, we prove that the sequence generated by proposed algorithm converges strongly to a common solution of equilibrium problems and fixed point problems. We use an effective self-adaptive step size rule to accelerate the convergence process of our proposed iterative algorithm. Moreover, some numerical results are given to show the effectiveness of the proposed algorithm. The results obtained in this paper extend and improve many recent ones in the literature.},\\nkeywords={Inertial method,  Subgradient extragradient method, Equilibrium probelm, Fixed point problem, Strong convergence},\\nabbrev_source_title={Optimization},\\n}\\n\\n\",\"author_short\":[\"Xie, Z.\",\"Cai, G.\",\"Tan, B.\"],\"key\":\"XCT_OPT24\",\"id\":\"XCT_OPT24\",\"bibbaseid\":\"xie-cai-tan-inertialsubgradientextragradientmethodforsolvingpseudomonotoneequilibriumprobelmsandfixedpointproblemsinhilbertspaces-2024\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/XCT-OPT2024.pdf\"},\"keyword\":[\"Inertial method\",\"Subgradient extragradient method\",\"Equilibrium probelm\",\"Fixed point problem\",\"Strong convergence\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Qin\"],\"firstnames\":[\"Xiaolong\"],\"suffixes\":[]}],\"title\":\"An alternated inertial algorithm with weak and linear convergence for solving monotone inclusions\",\"journal\":\"Annals of Mathematical Sciences and Applications\",\"year\":\"2023\",\"volume\":\"8\",\"number\":\"2\",\"pages\":\"321–345\",\"doi\":\"10.4310/AMSA.2023.v8.n2.a7\",\"url\":\"https://bingtan.me/files/paper/TQ-AMSA2023.pdf\",\"abstract\":\"Inertial-based methods have the drawback of not preserving the Fejér monotonicity of iterative sequences, which may result in slower convergence compared to their corresponding non-inertial versions. To overcome this issue, Mu and Peng [Stat. Optim. Inf. Comput. 3 (2015), 241–248; MR3393305] suggested an alternating inertial method that can recover the Fejér monotonicity of even subsequences. In this paper, we propose a modified version of the forward-backward algorithm with alternating inertial and relaxation effects to solve an inclusion problem in real Hilbert spaces. The weak and linear convergence of the presented algorithm is established under suitable and mild conditions on the involved operators and parameters. Furthermore, the Fejér monotonicity of even subsequences generated by the proposed algorithm with respect to the solution set is recovered. Finally, our tests on image restoration problems demonstrate the superiority of the proposed algorithm over some related results.\",\"keywords\":\"Inclusion problems, Alternated inertial, Forward-backward method, Tseng's method, Projection and contraction method, Linear convergence\",\"abbrev_source_title\":\"Ann. Math. Sci. Appl.\",\"bibtex\":\"@ARTICLE{TQ_AMSA23,\\nauthor={Tan, Bing and Qin, Xiaolong},\\ntitle={An alternated inertial algorithm with weak and linear convergence for solving monotone inclusions},\\njournal={Annals of Mathematical Sciences and Applications},\\nyear={2023},\\nvolume={8},\\nnumber={2},\\npages={321--345},\\ndoi={10.4310/AMSA.2023.v8.n2.a7},\\nurl={https://bingtan.me/files/paper/TQ-AMSA2023.pdf},\\nabstract={Inertial-based methods have the drawback of not preserving the Fejér monotonicity of iterative sequences, which may result in slower convergence compared to their corresponding non-inertial versions. To overcome this issue, Mu and Peng [Stat. Optim. Inf. Comput. 3 (2015), 241–248; MR3393305] suggested an alternating inertial method that can recover the Fejér monotonicity of even subsequences. In this paper, we propose a modified version of the forward-backward algorithm with alternating inertial and relaxation effects to solve an inclusion problem in real Hilbert spaces. The weak and linear convergence of the presented algorithm is established under suitable and mild conditions on the involved operators and parameters. Furthermore, the Fejér monotonicity of even subsequences generated by the proposed algorithm with respect to the solution set is recovered. Finally, our tests on image restoration problems demonstrate the superiority of the proposed algorithm over some related results.},\\nkeywords={Inclusion problems, Alternated inertial, Forward-backward method, Tseng's method, Projection and contraction method, Linear convergence},\\nabbrev_source_title={Ann. Math. Sci. Appl.},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Qin, X.\"],\"key\":\"TQ_AMSA23\",\"id\":\"TQ_AMSA23\",\"bibbaseid\":\"tan-qin-analternatedinertialalgorithmwithweakandlinearconvergenceforsolvingmonotoneinclusions-2023\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TQ-AMSA2023.pdf\"},\"keyword\":[\"Inclusion problems\",\"Alternated inertial\",\"Forward-backward method\",\"Tseng's method\",\"Projection and contraction method\",\"Linear convergence\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Qin\"],\"firstnames\":[\"Xiaolong\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Gibali\"],\"firstnames\":[\"Aviv\"],\"suffixes\":[]}],\"title\":\"Three approximation methods for solving constraint variational inequalities and related problems\",\"journal\":\"Pure and Applied Functional Analysis\",\"year\":\"2023\",\"volume\":\"8\",\"number\":\"3\",\"pages\":\"965–986\",\"url\":\"https://bingtan.me/files/paper/TGQ_PAFA2023.pdf\",\"abstract\":\"In this paper, we present three new self-adaptive one-projection algorithms to find common solutions for the pseudo-monotone variational inequality problem and the fixed point problem of a demi-contractive mapping. Note that the suggested approaches use a non-monotonic self-adaptive step size so that they can work well without knowing the prior knowledge of the Lipschitz constant of the mapping. Strong convergence theorems of the proposed iterative schemes are established in real Hilbert spaces. Several mathematical experiments are reported to demonstrate the numerical behavior of the suggested algorithms and compare them with the existing ones. Finally, the suggested methods are used to solve optimal control problems.\",\"keywords\":\"Variational inequality, Fixed point, Extragradient method, Hybrid steepest descent method, Pseudomonotone mapping\",\"abbrev_source_title\":\"Pure Appl. Funct. Anal.\",\"bibtex\":\"@ARTICLE{TGQ_PAFA23,\\nauthor={Tan, Bing and Qin, Xiaolong and Gibali, Aviv},\\ntitle={Three approximation methods for solving constraint variational inequalities and related problems},\\njournal={Pure and Applied Functional Analysis},\\nyear={2023},\\nvolume={8},\\nnumber={3},\\npages={965--986},\\nurl={https://bingtan.me/files/paper/TGQ_PAFA2023.pdf},\\nabstract={In this paper, we present three new self-adaptive one-projection algorithms to find common solutions for the pseudo-monotone variational inequality problem and the fixed point problem of a demi-contractive mapping. Note that the suggested approaches use a non-monotonic self-adaptive step size so that they can work well without knowing the prior knowledge of the Lipschitz constant of the mapping. Strong convergence theorems of the proposed iterative schemes are established in real Hilbert spaces. Several mathematical experiments are reported to demonstrate the numerical behavior of the suggested algorithms and compare them with the existing ones. Finally, the suggested methods are used to solve optimal control problems.},\\nkeywords={Variational inequality, Fixed point, Extragradient method, Hybrid steepest descent method, Pseudomonotone mapping},\\nabbrev_source_title={Pure Appl. Funct. Anal.},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Qin, X.\",\"Gibali, A.\"],\"key\":\"TGQ_PAFA23\",\"id\":\"TGQ_PAFA23\",\"bibbaseid\":\"tan-qin-gibali-threeapproximationmethodsforsolvingconstraintvariationalinequalitiesandrelatedproblems-2023\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TGQ_PAFA2023.pdf\"},\"keyword\":[\"Variational inequality\",\"Fixed point\",\"Extragradient method\",\"Hybrid steepest descent method\",\"Pseudomonotone mapping\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Li\"],\"firstnames\":[\"Songxiao\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Cho\"],\"firstnames\":[\"Sun\",\"Y.\"],\"suffixes\":[]}],\"title\":\"Inertial projection and contraction methods for pseudomonotone variational inequalities with non-Lipschitz operators and applications\",\"journal\":\"Applicable Analysis\",\"year\":\"2023\",\"volume\":\"102\",\"number\":\"4\",\"doi\":\"10.1080/00036811.2021.1979219\",\"pages\":\"1199–1221\",\"url\":\"https://bingtan.me/files/paper/TLC-AA2023.pdf\",\"abstract\":\"In this paper, some new accelerated iterative schemes are proposed to solve the variational inequality problem with a pseudomonotone and uniformly continuous operator in real Hilbert spaces. Strong convergence theorems of the suggested algorithms are obtained without the prior knowledge of the Lipschitz constant of the operator. Some numerical experiments and applications are performed to illustrate the advantages of the proposed methods with respect to several related ones.\",\"keywords\":\"Inertial extragradient method, Projection and contraction method, Pseudomonotone operator, Non-Lipschitz operator, Variational inequality problem\",\"abbrev_source_title\":\"Appl. Anal.\",\"bibtex\":\"@ARTICLE{TLC_AA23,\\nauthor={Tan, Bing and Li, Songxiao and Cho, Sun Y.},\\ntitle={Inertial projection and contraction methods for pseudomonotone variational inequalities with non-Lipschitz operators and applications},\\njournal={Applicable Analysis},\\nyear={2023},\\nvolume={102},\\nnumber={4},\\ndoi={10.1080/00036811.2021.1979219},\\npages={1199--1221},\\nurl={https://bingtan.me/files/paper/TLC-AA2023.pdf},\\nabstract={In this paper, some new accelerated iterative schemes are proposed to solve the variational inequality problem with a pseudomonotone and uniformly continuous operator in real Hilbert spaces. Strong convergence theorems of the suggested algorithms are obtained without the prior knowledge of the Lipschitz constant of the operator. Some numerical experiments and applications are performed to illustrate the advantages of the proposed methods with respect to several related ones.},\\nkeywords={Inertial extragradient method,  Projection and contraction method,  Pseudomonotone operator,  Non-Lipschitz operator,  Variational inequality problem},\\nabbrev_source_title={Appl. Anal.},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Li, S.\",\"Cho, S. Y.\"],\"key\":\"TLC_AA23\",\"id\":\"TLC_AA23\",\"bibbaseid\":\"tan-li-cho-inertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalitieswithnonlipschitzoperatorsandapplications-2023\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TLC-AA2023.pdf\"},\"keyword\":[\"Inertial extragradient method\",\"Projection and contraction method\",\"Pseudomonotone operator\",\"Non-Lipschitz operator\",\"Variational inequality problem\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Sunthrayuth\"],\"firstnames\":[\"Pongsakorn\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Cholamjiak\"],\"firstnames\":[\"Prasit\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Cho\"],\"firstnames\":[\"Yeol\",\"J.\"],\"suffixes\":[]}],\"title\":\"Modified inertial extragradient methods for finding minimum-norm solution of the variational inequality problem with applications to optimal control problem\",\"journal\":\"International Journal of Computer Mathematics\",\"year\":\"2023\",\"volume\":\"100\",\"number\":\"3\",\"pages\":\"525–545\",\"doi\":\"10.1080/00207160.2022.2137672\",\"url\":\"https://bingtan.me/files/paper/TSCC-IJCM23.pdf\",\"abstract\":\"In order to discover the minimum-norm solution of the pseudomonotone variational inequality problem in a real Hilbert space, we provide two variants of the inertial extragradient approach with a novel generalized adaptive step size. Two of the suggested algorithms make use of the projection and contraction methods. We demonstrate several strong convergence findings without requiring the prior knowledge of the Lipschitz constant of the mapping. Finally, we give a number of numerical examples that highlight the benefits and effectiveness of the suggested algorithms and how they may be used to solve the optimal control problem.\",\"keywords\":\"Variational inequality problem, Optimal control problem, Inertial method, Projection and contraction method\",\"abbrev_source_title\":\"Int. J. Comput. Math.\",\"bibtex\":\"@ARTICLE{TSCC_IJCM23,\\nauthor={Tan, Bing and Sunthrayuth, Pongsakorn and Cholamjiak, Prasit and  Cho, Yeol J.},\\ntitle={Modified inertial extragradient methods for finding minimum-norm solution of the variational inequality problem with applications to optimal control problem},\\njournal={International Journal of Computer Mathematics},\\nyear={2023},\\nvolume={100},\\nnumber={3},\\npages={525--545},\\ndoi={10.1080/00207160.2022.2137672},\\nurl={https://bingtan.me/files/paper/TSCC-IJCM23.pdf},\\nabstract={In order to discover the minimum-norm solution of the pseudomonotone variational inequality problem in a real Hilbert space, we provide two variants of the inertial extragradient approach with a novel generalized adaptive step size. Two of the suggested algorithms make use of the projection and contraction methods. We demonstrate several strong convergence findings without requiring the prior knowledge of the Lipschitz constant of the mapping. Finally, we give a number of numerical examples that highlight the benefits and effectiveness of the suggested algorithms and how they may be used to solve the optimal control problem.},\\nkeywords={Variational inequality problem, Optimal control problem, Inertial method, Projection and contraction method},\\nabbrev_source_title={Int. J. Comput. Math.},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Sunthrayuth, P.\",\"Cholamjiak, P.\",\"Cho, Y. J.\"],\"key\":\"TSCC_IJCM23\",\"id\":\"TSCC_IJCM23\",\"bibbaseid\":\"tan-sunthrayuth-cholamjiak-cho-modifiedinertialextragradientmethodsforfindingminimumnormsolutionofthevariationalinequalityproblemwithapplicationstooptimalcontrolproblem-2023\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TSCC-IJCM23.pdf\"},\"keyword\":[\"Variational inequality problem\",\"Optimal control problem\",\"Inertial method\",\"Projection and contraction method\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Li\"],\"firstnames\":[\"Songxiao\"],\"suffixes\":[]}],\"title\":\"Adaptive inertial subgradient extragradient methods for finding minimum-norm solutions of pseudomonotone variational inequalities\",\"journal\":\"Journal of Industrial and Management Optimization\",\"year\":\"2023\",\"volume\":\"19\",\"number\":\"10\",\"pages\":\"7640–7659\",\"doi\":\"10.3934/jimo.2022060\",\"url\":\"https://bingtan.me/files/paper/TL-JIMO2023.pdf\",\"abstract\":\"In this paper, four modified inertial subgradient extragradient methods with a new non-monotonic step size criterion are investigated for pseudomonotone variational inequality problems in real Hilbert spaces. Our algorithms employ two different step sizes in each iteration to update the values of iterative sequences, and they work well without the prior information about the Lipschitz constant of the operator. Strong convergence theorems of the proposed iterative schemes are established under some suitable and mild conditions. Some numerical examples are provided to demonstrate the computational efficiency and advantages of the proposed methods over other known ones.\",\"keywords\":\"Variational inequality problem, Inertial method, Extragradient method, Pseudomonotone operator, Non-Lipschitz operator\",\"abbrev_source_title\":\"J. Ind. Manag. Optim.\",\"bibtex\":\"@ARTICLE{TL_JIMO23,\\nauthor={Tan, Bing and Li, Songxiao},\\ntitle={Adaptive inertial subgradient extragradient methods for finding minimum-norm solutions of pseudomonotone variational inequalities},\\njournal={Journal of Industrial and Management Optimization},\\nyear={2023},\\nvolume={19},\\nnumber={10},\\npages={7640--7659},\\ndoi={10.3934/jimo.2022060},\\nurl={https://bingtan.me/files/paper/TL-JIMO2023.pdf},\\nabstract={In this paper, four modified inertial subgradient extragradient methods with a new non-monotonic step size criterion are investigated for pseudomonotone variational inequality problems in real Hilbert spaces. Our algorithms employ two different step sizes in each iteration to update the values of iterative sequences, and they work well without the prior information about the Lipschitz constant of the operator. Strong convergence theorems of the proposed iterative schemes are established under some suitable and mild conditions. Some numerical examples are provided to demonstrate the computational efficiency and advantages of the proposed methods over other known ones.},\\nkeywords={Variational inequality problem, Inertial method, Extragradient method, Pseudomonotone operator, Non-Lipschitz operator},\\nabbrev_source_title={J. Ind. Manag. Optim.},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Li, S.\"],\"key\":\"TL_JIMO23\",\"id\":\"TL_JIMO23\",\"bibbaseid\":\"tan-li-adaptiveinertialsubgradientextragradientmethodsforfindingminimumnormsolutionsofpseudomonotonevariationalinequalities-2023\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TL-JIMO2023.pdf\"},\"keyword\":[\"Variational inequality problem\",\"Inertial method\",\"Extragradient method\",\"Pseudomonotone operator\",\"Non-Lipschitz operator\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Zhou\"],\"firstnames\":[\"Zheng\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Li\"],\"firstnames\":[\"Songxiao\"],\"suffixes\":[]}],\"title\":\"Inertial algorithms with adaptive stepsizes for split variational inclusion problems and their applications to signal recovery problem\",\"journal\":\"Mathematical Methods in the Applied Sciences\",\"year\":\"2023\",\"volume\":\"doi:10.1002/mma.9436\",\"doi\":\"10.1002/mma.9436\",\"url\":\"https://bingtan.me/files/paper/ZTL-MMAS2023.pdf\",\"abstract\":\"With the help of the Meir-Keeler contraction method and the Mann-type method, two adaptive inertial iterative schemes are introduced for finding solutions of the split variational inclusion problem in Hilbert spaces. The strong convergence of the suggested algorithms is guaranteed by a new stepsize criterion that does not require calculation of the bounded linear operator norm. Some numerical experiments and applications in signal recovery problems are given to demonstrate the efficiency of the proposed algorithms.\",\"keywords\":\"Adaptive stepsize, Inertial method, Mann method, Meir-Keeler contraction, Signal recovery, Split variational inclusion problem\",\"abbrev_source_title\":\"Math. Methods Appl. Sci.\",\"bibtex\":\"@ARTICLE{ZTL_MMAS23,\\nauthor={Zhou, Zheng and Tan, Bing and Li, Songxiao},\\ntitle={Inertial algorithms with adaptive stepsizes for split variational inclusion problems and their applications to signal recovery problem},\\njournal={Mathematical Methods in the Applied Sciences},\\nyear={2023},\\nvolume={doi:10.1002/mma.9436},\\ndoi={10.1002/mma.9436},\\nurl={https://bingtan.me/files/paper/ZTL-MMAS2023.pdf},\\nabstract={With the help of the Meir-Keeler contraction method and the Mann-type method, two adaptive inertial iterative schemes are introduced for finding solutions of the split variational inclusion problem in Hilbert spaces. The strong convergence of the suggested algorithms is guaranteed by a new stepsize criterion that does not require calculation of the bounded linear operator norm. Some numerical experiments and applications in signal recovery problems are given to demonstrate the efficiency of the proposed algorithms.},\\nkeywords={Adaptive stepsize, Inertial method, Mann method, Meir-Keeler contraction, Signal recovery, Split variational inclusion problem},\\nabbrev_source_title={Math. Methods Appl. Sci.},\\n}\\n\\n\",\"author_short\":[\"Zhou, Z.\",\"Tan, B.\",\"Li, S.\"],\"key\":\"ZTL_MMAS23\",\"id\":\"ZTL_MMAS23\",\"bibbaseid\":\"zhou-tan-li-inertialalgorithmswithadaptivestepsizesforsplitvariationalinclusionproblemsandtheirapplicationstosignalrecoveryproblem-2023\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/ZTL-MMAS2023.pdf\"},\"keyword\":[\"Adaptive stepsize\",\"Inertial method\",\"Mann method\",\"Meir-Keeler contraction\",\"Signal recovery\",\"Split variational inclusion problem\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Luo\"],\"firstnames\":[\"Yinglin\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Li\"],\"firstnames\":[\"Songxiao\"],\"suffixes\":[]}],\"title\":\"Inertial splitting algorithms for nonlinear operators of pseudocontractive and accretive types\",\"journal\":\"Optimization\",\"year\":\"2023\",\"volume\":\"72\",\"number\":\"3\",\"pages\":\"647–675\",\"doi\":\"10.1080/02331934.2021.1981896\",\"url\":\"https://bingtan.me/files/paper/LTL-OPT2023.pdf\",\"abstract\":\"In this paper, inertial splitting algorithms for nonlinear operators of pseudocontractive and accretive types are proposed. Weak and strong convergence theorems are established in uniformly convex and $q$-uniformly smooth Banach spaces. Numerical examples are given to illustrate the effectiveness of our proposed algorithms.\",\"keywords\":\"Accretive operator, Banach space, Inertial method, Strict pseudo-contraction, Strong convergence\",\"abbrev_source_title\":\"Optimization\",\"bibtex\":\"@ARTICLE{LTL_OPT23,\\nauthor={Luo, Yinglin and Tan, Bing and Li, Songxiao},\\ntitle={Inertial splitting algorithms for nonlinear operators of pseudocontractive and accretive types},\\njournal={Optimization},\\nyear={2023},\\nvolume={72},\\nnumber={3},\\npages={647--675},\\ndoi={10.1080/02331934.2021.1981896},\\nurl={https://bingtan.me/files/paper/LTL-OPT2023.pdf},\\nabstract={In this paper, inertial splitting algorithms for nonlinear operators of pseudocontractive and accretive types are proposed. Weak and strong convergence theorems are established in uniformly convex and $q$-uniformly smooth Banach spaces. Numerical examples are given to illustrate the effectiveness of our proposed algorithms.},\\nkeywords={Accretive operator,  Banach space,  Inertial method,  Strict pseudo-contraction,  Strong convergence},\\nabbrev_source_title={Optimization},\\n}\\n\\n\",\"author_short\":[\"Luo, Y.\",\"Tan, B.\",\"Li, S.\"],\"key\":\"LTL_OPT23\",\"id\":\"LTL_OPT23\",\"bibbaseid\":\"luo-tan-li-inertialsplittingalgorithmsfornonlinearoperatorsofpseudocontractiveandaccretivetypes-2023\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/LTL-OPT2023.pdf\"},\"keyword\":[\"Accretive operator\",\"Banach space\",\"Inertial method\",\"Strict pseudo-contraction\",\"Strong convergence\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Zhou\"],\"firstnames\":[\"Xiaolin\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Cai\"],\"firstnames\":[\"Gang\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Dong\"],\"firstnames\":[\"Qiao\",\"L.\"],\"suffixes\":[]}],\"title\":\"A modified generalized version of projected reflected gradient method in Hilbert spaces\",\"journal\":\"Numerical Algorithms\",\"year\":\"2023\",\"volume\":\"doi:10.1007/s11075-023-01566-1\",\"doi\":\"10.1007/s11075-023-01566-1\",\"url\":\"https://bingtan.me/files/paper/ZCTD-NUMA2023.pdf\",\"abstract\":\"This article is concerned with a universal version of projected reflected gradient method with new step size for solving variational inequality problem in Hilbert spaces. Under appropriate assumptions controlled by the operators and parameters, we acquire the weak convergence of the proposed algorithm. We establish an R-linear convergence rate of our method on the condition that the relevant mapping is strongly monotone. We rework our first algorithm so that it can be simplified to several generalized methods in the literature. The efficacy and availability of our proposed iterative scheme are demonstrated in numerical experiments.\",\"keywords\":\"Projected reflected gradient method, Variational inequality, Weak and linear convergence, Hilbert spaces\",\"abbrev_source_title\":\"Numer. Algorithms\",\"bibtex\":\"@ARTICLE{ZCTD_NUMA23,\\nauthor={Zhou, Xiaolin and Cai, Gang and Tan, Bing and Dong, Qiao L.},\\ntitle={A modified generalized version of projected reflected gradient method in Hilbert spaces},\\njournal={Numerical Algorithms},\\nyear={2023},\\nvolume={doi:10.1007/s11075-023-01566-1},\\ndoi={10.1007/s11075-023-01566-1},\\nurl={https://bingtan.me/files/paper/ZCTD-NUMA2023.pdf},\\nabstract={This article is concerned with a universal version of projected reflected gradient method with new step size for solving variational inequality problem in Hilbert spaces. Under appropriate assumptions controlled by the operators and parameters, we acquire the weak convergence of the proposed algorithm. We establish an R-linear convergence rate of our method on the condition that the relevant mapping is strongly monotone. We rework our first algorithm so that it can be simplified to several generalized methods in the literature. The efficacy and availability of our proposed iterative scheme are demonstrated in numerical experiments.},\\nkeywords={Projected reflected gradient method, Variational inequality, Weak and linear convergence, Hilbert spaces},\\nabbrev_source_title={Numer. Algorithms},\\n}\\n\\n\",\"author_short\":[\"Zhou, X.\",\"Cai, G.\",\"Tan, B.\",\"Dong, Q. L.\"],\"key\":\"ZCTD_NUMA23\",\"id\":\"ZCTD_NUMA23\",\"bibbaseid\":\"zhou-cai-tan-dong-amodifiedgeneralizedversionofprojectedreflectedgradientmethodinhilbertspaces-2023\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/ZCTD-NUMA2023.pdf\"},\"keyword\":[\"Projected reflected gradient method\",\"Variational inequality\",\"Weak and linear convergence\",\"Hilbert spaces\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Hu\"],\"firstnames\":[\"Shaotao\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Wang\"],\"firstnames\":[\"Yuanheng\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Wang\"],\"firstnames\":[\"Fenghui\"],\"suffixes\":[]}],\"title\":\"Inertial iterative method for solving variational inequality problems of pseudo-monotone operators and fixed point problems of nonexpansive mappings in Hilbert spaces\",\"journal\":\"Journal of Industrial and Management Optimization\",\"year\":\"2023\",\"volume\":\"19\",\"number\":\"4\",\"pages\":\"2655–2675\",\"doi\":\"10.3934/jimo.2022060\",\"url\":\"https://bingtan.me/files/paper/HWTW-JIMO2023.pdf\",\"abstract\":\"In this paper, we propose a new inertial viscosity iterative algorithm for solving the variational inequality problem with a pseudo-monotone operator and the fixed point problem involving a nonexpansive mapping in real Hilbert spaces. The advantage of the proposed algorithm is that it can work without the prior knowledge of the Lipschitz constant of the mapping. The strong convergence of the sequence generated by the proposed algorithm is proved under some suitable assumptions imposed on the parameters. Some numerical experiments are given to support our main results.\",\"keywords\":\"Inertial method, Viscosity method, Strong convergence, Variational inequality problem, Fixed point problem, Nonexpansive mapping, Pseudomonotone operator\",\"abbrev_source_title\":\"J. Ind. Manag. Optim.\",\"bibtex\":\"@ARTICLE{HWTW_JIMO23,\\nauthor={Hu, Shaotao and Wang, Yuanheng and Tan, Bing and Wang, Fenghui},\\ntitle={Inertial iterative method for solving variational inequality problems of pseudo-monotone operators and fixed point problems of nonexpansive mappings in {H}ilbert spaces},\\njournal={Journal of Industrial and Management Optimization},\\nyear={2023},\\nvolume={19},\\nnumber={4},\\npages={2655--2675},\\ndoi={10.3934/jimo.2022060},\\nurl={https://bingtan.me/files/paper/HWTW-JIMO2023.pdf},\\nabstract={In this paper, we propose a new inertial viscosity iterative algorithm for solving the variational inequality problem with a pseudo-monotone operator and the fixed point problem involving a nonexpansive mapping in real Hilbert spaces. The advantage of the proposed algorithm is that it can work without the prior knowledge of the Lipschitz constant of the mapping. The strong convergence of the sequence generated by the proposed algorithm is proved under some suitable assumptions imposed on the parameters. Some numerical experiments are given to support our main results.},\\nkeywords={Inertial method,  Viscosity method,  Strong convergence, Variational inequality problem, Fixed point problem, Nonexpansive mapping, Pseudomonotone operator},\\nabbrev_source_title={J. Ind. Manag. Optim.},\\n}\\n\\n\",\"author_short\":[\"Hu, S.\",\"Wang, Y.\",\"Tan, B.\",\"Wang, F.\"],\"key\":\"HWTW_JIMO23\",\"id\":\"HWTW_JIMO23\",\"bibbaseid\":\"hu-wang-tan-wang-inertialiterativemethodforsolvingvariationalinequalityproblemsofpseudomonotoneoperatorsandfixedpointproblemsofnonexpansivemappingsinhilbertspaces-2023\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/HWTW-JIMO2023.pdf\"},\"keyword\":[\"Inertial method\",\"Viscosity method\",\"Strong convergence\",\"Variational inequality problem\",\"Fixed point problem\",\"Nonexpansive mapping\",\"Pseudomonotone operator\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Qin\"],\"firstnames\":[\"Xiaolong\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Cho\"],\"firstnames\":[\"Sun\",\"Y.\"],\"suffixes\":[]}],\"title\":\"Revisiting subgradient extragradient methods for solving variational inequalities\",\"journal\":\"Numerical Algorithms\",\"year\":\"2022\",\"volume\":\"90\",\"number\":\"4\",\"pages\":\"1593–1615\",\"doi\":\"10.1007/s11075-021-01243-1\",\"url\":\"https://bingtan.me/files/paper/TQC-NUMA2022.pdf\",\"abstract\":\"In this paper, several extragradient algorithms with inertial effects and adaptive non-monotonic step sizes are proposed to solve pseudomonotone variational inequalities in real Hilbert spaces. The strong convergence of the proposed methods is established without the prior knowledge of the Lipschitz constant of the mapping. Some numerical experiments are given to illustrate the advantages and efficiency of the proposed schemes over previously known ones.\",\"keywords\":\"Armijo stepsize, Inertial extragradient method, Non-Lipschitz operator, Pseudomonotone operator, Variational inequality problem\",\"abbrev_source_title\":\"Numer. Algorithms\",\"bibtex\":\"@ARTICLE{TQC_NUMA22,\\nauthor={Tan, Bing and Qin, Xiaolong and Cho, Sun Y.},\\ntitle={Revisiting subgradient extragradient methods for solving variational inequalities},\\njournal={Numerical Algorithms},\\nyear={2022},\\nvolume={90},\\nnumber={4},\\npages={1593--1615},\\ndoi={10.1007/s11075-021-01243-1},\\nurl={https://bingtan.me/files/paper/TQC-NUMA2022.pdf},\\nabstract={In this paper, several extragradient algorithms with inertial effects and adaptive non-monotonic step sizes are proposed to solve pseudomonotone variational inequalities in real Hilbert spaces. The strong convergence of the proposed methods is established without the prior knowledge of the Lipschitz constant of the mapping. Some numerical experiments are given to illustrate the advantages and efficiency of the proposed schemes over previously known ones.},\\nkeywords={Armijo stepsize,  Inertial extragradient method,  Non-Lipschitz operator,  Pseudomonotone operator,  Variational inequality problem},\\nabbrev_source_title={Numer. Algorithms},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Qin, X.\",\"Cho, S. Y.\"],\"key\":\"TQC_NUMA22\",\"id\":\"TQC_NUMA22\",\"bibbaseid\":\"tan-qin-cho-revisitingsubgradientextragradientmethodsforsolvingvariationalinequalities-2022\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TQC-NUMA2022.pdf\"},\"keyword\":[\"Armijo stepsize\",\"Inertial extragradient method\",\"Non-Lipschitz operator\",\"Pseudomonotone operator\",\"Variational inequality problem\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"downloads\":2,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Qin\"],\"firstnames\":[\"Xiaolong\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Yao\"],\"firstnames\":[\"Jen\",\"C.\"],\"suffixes\":[]}],\"title\":\"Strong convergence of inertial projection and contraction methods for pseudomonotone variational inequalities with applications to optimal control problems\",\"journal\":\"Journal of Global Optimization\",\"year\":\"2022\",\"volume\":\"82\",\"number\":\"3\",\"pages\":\"523–557\",\"doi\":\"10.1007/s10898-021-01095-y\",\"url\":\"https://bingtan.me/files/paper/TQY-JOGO2022.pdf\",\"abstract\":\"This paper investigates some inertial projection and contraction methods for solving pseudomonotone variational inequality problems in real Hilbert spaces. The algorithms use a new non-monotonic step size so that they can work without the prior knowledge of the Lipschitz constant of the operator. Strong convergence theorems of the suggested algorithms are obtained under some suitable conditions. Some numerical experiments in finite- and infinite-dimensional spaces and applications in optimal control problems are implemented to demonstrate the performance of the suggested schemes and we also compare them with several related results.\",\"keywords\":\"Inertial method, Optimal control problem, Projection and contraction method, Pseudomonotone operator, Subgradient extragradient method, Variational inequality problem\",\"abbrev_source_title\":\"J. Global Optim.\",\"bibtex\":\"@ARTICLE{TQY_JOGO22,\\nauthor={Tan, Bing and Qin, Xiaolong and Yao, Jen C.},\\ntitle={Strong convergence of inertial projection and contraction methods for pseudomonotone variational inequalities with applications to optimal control problems},\\njournal={Journal of Global Optimization},\\nyear={2022},\\nvolume={82},\\nnumber={3},\\npages={523--557},\\ndoi={10.1007/s10898-021-01095-y},\\nurl={https://bingtan.me/files/paper/TQY-JOGO2022.pdf},\\nabstract={This paper investigates some inertial projection and contraction methods for solving pseudomonotone variational inequality problems in real Hilbert spaces. The algorithms use a new non-monotonic step size so that they can work without the prior knowledge of the Lipschitz constant of the operator. Strong convergence theorems of the suggested algorithms are obtained under some suitable conditions. Some numerical experiments in finite- and infinite-dimensional spaces and applications in optimal control problems are implemented to demonstrate the performance of the suggested schemes and we also compare them with several related results.},\\nkeywords={Inertial method,  Optimal control problem,  Projection and contraction method,  Pseudomonotone operator,  Subgradient extragradient method,  Variational inequality problem},\\nabbrev_source_title={J. Global Optim.},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Qin, X.\",\"Yao, J. C.\"],\"key\":\"TQY_JOGO22\",\"id\":\"TQY_JOGO22\",\"bibbaseid\":\"tan-qin-yao-strongconvergenceofinertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalitieswithapplicationstooptimalcontrolproblems-2022\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TQY-JOGO2022.pdf\"},\"keyword\":[\"Inertial method\",\"Optimal control problem\",\"Projection and contraction method\",\"Pseudomonotone operator\",\"Subgradient extragradient method\",\"Variational inequality problem\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Qin\"],\"firstnames\":[\"Xiaolong\"],\"suffixes\":[]}],\"title\":\"Modified inertial projection and contraction algorithms for solving variational inequality problems with non-Lipschitz continuous operators\",\"journal\":\"Analysis and Mathematical Physics\",\"year\":\"2022\",\"volume\":\"12\",\"number\":\"1\",\"doi\":\"10.1007/s13324-021-00638-6\",\"pages\":\"26\",\"url\":\"https://bingtan.me/files/paper/TQ-AMP2022.pdf\",\"abstract\":\"In this paper, we present four modified inertial projection and contraction methods to solve the variational inequality problem with a pseudo-monotone and non-Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems of the proposed algorithms are established without the prior knowledge of the Lipschitz constant of the operator. Several numerical experiments and the applications to optimal control problems are provided to verify the advantages and efficiency of the proposed algorithms.\",\"keywords\":\"Inertial method, Projection and contraction method, Pseudomonotone operator, Subgradient extragradient method, Non-Lipschitz operator, Variational inequality problem\",\"abbrev_source_title\":\"Anal. Math. Phys.\",\"bibtex\":\"@ARTICLE{TQ_AMP22,\\nauthor={Tan, Bing and Qin, Xiaolong},\\ntitle={Modified inertial projection and contraction algorithms for solving variational inequality problems with non-Lipschitz continuous operators},\\njournal={Analysis and Mathematical Physics},\\nyear={2022},\\nvolume={12},\\nnumber={1},\\ndoi={10.1007/s13324-021-00638-6},\\npages={26},\\nurl={https://bingtan.me/files/paper/TQ-AMP2022.pdf},\\nabstract={In this paper, we present four modified inertial projection and contraction methods to solve the variational inequality problem with a pseudo-monotone and non-Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems of the proposed algorithms are established without the prior knowledge of the Lipschitz constant of the operator. Several numerical experiments and the applications to optimal control problems are provided to verify the advantages and efficiency of the proposed algorithms.},\\nkeywords={Inertial method,  Projection and contraction method,  Pseudomonotone operator,  Subgradient extragradient method,  Non-Lipschitz operator,  Variational inequality problem},\\nabbrev_source_title={Anal. Math. Phys.},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Qin, X.\"],\"key\":\"TQ_AMP22\",\"id\":\"TQ_AMP22\",\"bibbaseid\":\"tan-qin-modifiedinertialprojectionandcontractionalgorithmsforsolvingvariationalinequalityproblemswithnonlipschitzcontinuousoperators-2022\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TQ-AMP2022.pdf\"},\"keyword\":[\"Inertial method\",\"Projection and contraction method\",\"Pseudomonotone operator\",\"Subgradient extragradient method\",\"Non-Lipschitz operator\",\"Variational inequality problem\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Petruşel\"],\"firstnames\":[\"Adrian\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Qin\"],\"firstnames\":[\"Xiaolong\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Yao\"],\"firstnames\":[\"Jen\",\"C.\"],\"suffixes\":[]}],\"title\":\"Global and linear convergence of alternated inertial single projection algorithms for pseudo-monotone variational inequalities\",\"journal\":\"Fixed Point Theory\",\"year\":\"2022\",\"volume\":\"23\",\"number\":\"1\",\"pages\":\"391–426\",\"doi\":\"10.24193/fpt-ro.2022.1.25\",\"url\":\"https://bingtan.me/files/paper/TPQY-FPT2022.pdf\",\"abstract\":\"In this paper, we investigate three new relaxed single projection methods with alternating inertial extrapolation steps and adaptive non-monotonic step sizes for solving pseudo-monotone variational inequalities in real Hilbert spaces. The proposed algorithms need to compute the projection on the feasible set only once in each iteration and they can work adaptively without the prior information of the Lipschitz constant of the mapping. The weak convergence theorems of the proposed iterative schemes are established under some appropriate conditions imposed on the parameters. These methods recover the Fejér monotonicity of the even subsequence with respect to the solution and obtain linear convergence rates. Finally, some numerical experiments and applications to optimal control problems are provided to demonstrate the advantages and efficiency of the proposed methods compared to some recent related ones.\",\"keywords\":\"Adaptive stepsize, Alternated inertial method, Projection and contraction method, Pseudomonotone operator, Subgradient extragradient method, Variational inequality problem\",\"abbrev_source_title\":\"Fixed Point Theory\",\"bibtex\":\"@ARTICLE{TPQY_FPT22,\\nauthor={Tan, Bing and Petruşel, Adrian and Qin, Xiaolong and Yao, Jen C.},\\ntitle={Global and linear convergence of alternated inertial single projection algorithms for pseudo-monotone variational inequalities},\\njournal={Fixed Point Theory},\\nyear={2022},\\nvolume={23},\\nnumber={1},\\npages={391--426},\\ndoi={10.24193/fpt-ro.2022.1.25},\\nurl={https://bingtan.me/files/paper/TPQY-FPT2022.pdf},\\nabstract={In this paper, we investigate three new relaxed single projection methods with alternating inertial extrapolation steps and adaptive non-monotonic step sizes for solving pseudo-monotone variational inequalities in real Hilbert spaces. The proposed algorithms need to compute the projection on the feasible set only once in each iteration and they can work adaptively without the prior information of the Lipschitz constant of the mapping. The weak convergence theorems of the proposed iterative schemes are established under some appropriate conditions imposed on the parameters. These methods recover the Fejér monotonicity of the even subsequence with respect to the solution and obtain linear convergence rates. Finally, some numerical experiments and applications to optimal control problems are provided to demonstrate the advantages and efficiency of the proposed methods compared to some recent related ones.},\\nkeywords={Adaptive stepsize,  Alternated inertial method,  Projection and contraction method,  Pseudomonotone operator,  Subgradient extragradient method,  Variational inequality problem},\\nabbrev_source_title={Fixed Point Theory},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Petruşel, A.\",\"Qin, X.\",\"Yao, J. C.\"],\"key\":\"TPQY_FPT22\",\"id\":\"TPQY_FPT22\",\"bibbaseid\":\"tan-petruel-qin-yao-globalandlinearconvergenceofalternatedinertialsingleprojectionalgorithmsforpseudomonotonevariationalinequalities-2022\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TPQY-FPT2022.pdf\"},\"keyword\":[\"Adaptive stepsize\",\"Alternated inertial method\",\"Projection and contraction method\",\"Pseudomonotone operator\",\"Subgradient extragradient method\",\"Variational inequality problem\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"downloads\":2,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Qin\"],\"firstnames\":[\"Xiaolong\"],\"suffixes\":[]}],\"title\":\"Adaptive modified inertial projection and contraction methods for pseudomonotone variational inequalities\",\"journal\":\"Journal of Applied and Numerical Optimization\",\"year\":\"2022\",\"volume\":\"4\",\"number\":\"2\",\"pages\":\"221–243\",\"doi\":\"10.23952/jano.4.2022.2.08\",\"url\":\"https://bingtan.me/files/paper/TQ-JANO2022.pdf\",\"abstract\":\"To handle pseudomonotone variational inequality problems in real Hilbert spaces, four modified inertial projection and contraction algorithms with non-monotonic step sizes are suggested in this paper. The proposed algorithms take advantage of a novel non-monotonic step size criteria, allowing them to work without previous knowledge of the Lipschitz constant of the mapping involved. Under certain situations, the strong convergence of the iterative sequences generated by the suggested algorithms is established. Finally, several numerical experiments are offered to validate the theoretical conclusions.\",\"keywords\":\"Inertial method, Pseudomonotone operator, Projection and contraction method, Subgradient extragradient method, Variational inequality problem\",\"abbrev_source_title\":\"J. Appl. Numer. Optim.\",\"bibtex\":\"@ARTICLE{TQ_JANO22,\\nauthor={Tan, Bing and Qin, Xiaolong},\\ntitle={Adaptive modified inertial projection and contraction methods for pseudomonotone variational inequalities},\\njournal={Journal of Applied and Numerical Optimization},\\nyear={2022},\\nvolume={4},\\nnumber={2},\\npages={221--243},\\ndoi={10.23952/jano.4.2022.2.08},\\nurl={https://bingtan.me/files/paper/TQ-JANO2022.pdf},\\nabstract={To handle pseudomonotone variational inequality problems in real Hilbert spaces, four modified inertial projection and contraction algorithms with non-monotonic step sizes are suggested in this paper. The proposed algorithms take advantage of a novel non-monotonic step size criteria, allowing them to work without previous knowledge of the Lipschitz constant of the mapping involved. Under certain situations, the strong convergence of the iterative sequences generated by the suggested algorithms is established. Finally, several numerical experiments are offered to validate the theoretical conclusions.},\\nkeywords={Inertial method, Pseudomonotone operator, Projection and contraction method, Subgradient extragradient method, Variational inequality problem},\\nabbrev_source_title={J. Appl. Numer. Optim.},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Qin, X.\"],\"key\":\"TQ_JANO22\",\"id\":\"TQ_JANO22\",\"bibbaseid\":\"tan-qin-adaptivemodifiedinertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalities-2022\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TQ-JANO2022.pdf\"},\"keyword\":[\"Inertial method\",\"Pseudomonotone operator\",\"Projection and contraction method\",\"Subgradient extragradient method\",\"Variational inequality problem\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Qin\"],\"firstnames\":[\"Xiaolong\"],\"suffixes\":[]}],\"title\":\"Self adaptive viscosity-type inertial extragradient algorithms for solving variational inequalities with applications\",\"journal\":\"Mathematical Modelling and Analysis\",\"year\":\"2022\",\"volume\":\"27\",\"number\":\"1\",\"pages\":\"41–58\",\"doi\":\"10.3846/mma.2022.13846\",\"url\":\"https://bingtan.me/files/paper/TQ-MMA2022.pdf\",\"abstract\":\"In this paper, we introduce two new inertial extragradient algorithms with non-monotonic stepsizes for solving monotone and Lipschitz continuous variational inequality problems in real Hilbert spaces. Strong convergence theorems of the suggested iterative schemes are established without the prior knowledge of the Lipschitz constant of the mapping. Finally, some numerical examples are provided to illustrate the efficiency and advantages of the proposed algorithms and compare them with some related ones.\",\"keywords\":\"Inertial method, Subgradient extragradient method, Tseng's extragradient method, Optimal control problem, Variational inequality problem, Viscosity method\",\"abbrev_source_title\":\"Math. Model. Anal.\",\"bibbase_note\":\"<span style=\\\"color: red\\\">(<s>ESI Highly Cited Paper</s>)</span>\",\"bibtex\":\"@ARTICLE{TQ_MMA22,\\nauthor={Tan, Bing and Qin, Xiaolong},\\ntitle={Self adaptive viscosity-type inertial extragradient algorithms for solving variational inequalities with applications},\\njournal={Mathematical Modelling and Analysis},\\nyear={2022},\\nvolume={27},\\nnumber={1},\\npages={41--58},\\ndoi={10.3846/mma.2022.13846},\\nurl={https://bingtan.me/files/paper/TQ-MMA2022.pdf},\\nabstract={In this paper, we introduce two new inertial extragradient algorithms with non-monotonic stepsizes for solving monotone and Lipschitz continuous variational inequality problems in real Hilbert spaces. Strong convergence theorems of the suggested iterative schemes are established without the prior knowledge of the Lipschitz constant of the mapping. Finally, some numerical examples are provided to illustrate the efficiency and advantages of the proposed algorithms and compare them with some related ones.},\\nkeywords={Inertial method, Subgradient extragradient method,  Tseng's extragradient method,  Optimal control problem,  Variational inequality problem,  Viscosity method},\\nabbrev_source_title={Math. Model. Anal.},\\nbibbase_note={<span style=\\\"color: red\\\">(<s>ESI Highly Cited Paper</s>)</span>},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Qin, X.\"],\"key\":\"TQ_MMA22\",\"id\":\"TQ_MMA22\",\"bibbaseid\":\"tan-qin-selfadaptiveviscositytypeinertialextragradientalgorithmsforsolvingvariationalinequalitieswithapplications-2022\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TQ-MMA2022.pdf\"},\"keyword\":[\"Inertial method\",\"Subgradient extragradient method\",\"Tseng's extragradient method\",\"Optimal control problem\",\"Variational inequality problem\",\"Viscosity method\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Liu\"],\"firstnames\":[\"Liya\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Qin\"],\"firstnames\":[\"Xiaolong\"],\"suffixes\":[]}],\"title\":\"Strong convergence of inertial extragradient algorithms for solving variational inequalities and fixed point problems\",\"journal\":\"Fixed Point Theory\",\"year\":\"2022\",\"volume\":\"23\",\"number\":\"2\",\"pages\":\"707–728\",\"doi\":\"10.24193/fpt-ro.2022.2.17\",\"url\":\"https://bingtan.me/files/paper/TLQ-FPT2022.pdf\",\"abstract\":\"This paper investigates two inertial extragradient algorithms for seeking a common solution to a variational inequality problem involving a monotone and Lipschitz continuous mapping and a fixed point problem with a demicontractive mapping in real Hilbert spaces. Our algorithms need to calculate the projection on the feasible set only once in each iteration. Moreover, they can work well without the prior information of the Lipschitz constant of the operator and do not contain any linesearch process. Strong convergence theorems of the suggested algorithms are established under suitable conditions. Some experiments are presented to illustrate the numerical efficiency of the suggested algorithms and compare them with some existing ones.\",\"keywords\":\"Variational inequality problem, Fixed point problem, Subgradient extragradient method, Tseng's extragradient method, Inertial method, Demicontractive mapping\",\"abbrev_source_title\":\"Fixed Point Theory\",\"bibtex\":\"@ARTICLE{TLQ_FPT22,\\nauthor={Tan, Bing and Liu, Liya and Qin, Xiaolong},\\ntitle={Strong convergence of inertial extragradient algorithms for solving variational inequalities and fixed point problems},\\njournal={Fixed Point Theory},\\nyear={2022},\\nvolume={23},\\nnumber={2},\\npages={707--728},\\ndoi={10.24193/fpt-ro.2022.2.17},\\nurl={https://bingtan.me/files/paper/TLQ-FPT2022.pdf},\\nabstract={This paper investigates two inertial extragradient algorithms for seeking a common solution to a variational inequality problem involving a monotone and Lipschitz continuous mapping and a fixed point problem with a demicontractive mapping in real Hilbert spaces. Our algorithms need to calculate the projection on the feasible set only once in each iteration. Moreover, they can work well without the prior information of the Lipschitz constant of the operator and do not contain any linesearch process. Strong convergence theorems of the suggested algorithms are established under suitable conditions. Some experiments are presented to illustrate the numerical efficiency of the suggested algorithms and compare them with some existing ones.},\\nkeywords={Variational inequality problem, Fixed point problem, Subgradient extragradient method, Tseng's extragradient method, Inertial method, Demicontractive mapping},\\nabbrev_source_title={Fixed Point Theory},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Liu, L.\",\"Qin, X.\"],\"key\":\"TLQ_FPT22\",\"id\":\"TLQ_FPT22\",\"bibbaseid\":\"tan-liu-qin-strongconvergenceofinertialextragradientalgorithmsforsolvingvariationalinequalitiesandfixedpointproblems-2022\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TLQ-FPT2022.pdf\"},\"keyword\":[\"Variational inequality problem\",\"Fixed point problem\",\"Subgradient extragradient method\",\"Tseng's extragradient method\",\"Inertial method\",\"Demicontractive mapping\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Li\"],\"firstnames\":[\"Songxiao\"],\"suffixes\":[]}],\"title\":\"Modified inertial projection and contraction algorithms with non-monotonic step sizes for solving variational inequalities and their applications\",\"journal\":\"Optimization\",\"year\":\"2022\",\"volume\":\"doi:10.1080/02331934.2022.2123705\",\"doi\":\"10.1080/02331934.2022.2123705\",\"url\":\"https://bingtan.me/files/paper/TL-OPT2022.pdf\",\"abstract\":\"We present two adaptive inertial projection and contraction algorithms to discover the minimum-norm solutions of pseudomonotone variational inequality problems in real Hilbert spaces. The suggested algorithms employ two different step sizes in each iteration and use a non-monotone step size criterion without any line search allowing them to work adaptively. The strong convergence of the iterative sequences formed by the proposed algorithms is established under some mild conditions. Several numerical experiments occurring in finite- and infinite-dimensional Hilbert spaces and applications to optimal control problems as well as signal processing problems are given. Performance profiles are used to verify the computational efficiency and advantages of the proposed algorithms with respect to some known ones.\",\"keywords\":\"Variational inequality problem, Inertial method, Projection and contraction method, Subgradient extragradient method, Pseudomonotone operator, Optimal control problem, Signal processing problem, Strong convergence\",\"abbrev_source_title\":\"Optimization\",\"bibtex\":\"@ARTICLE{TL_OPT22,\\nauthor={Tan, Bing and Li, Songxiao},\\ntitle={Modified inertial projection and contraction algorithms with non-monotonic step sizes for solving variational inequalities and their applications},\\njournal={Optimization},\\nyear={2022},\\nvolume={doi:10.1080/02331934.2022.2123705},\\ndoi={10.1080/02331934.2022.2123705},\\nurl={https://bingtan.me/files/paper/TL-OPT2022.pdf},\\nabstract={We present two adaptive inertial projection and contraction algorithms to discover the minimum-norm solutions of pseudomonotone variational inequality problems in real Hilbert spaces. The suggested algorithms employ two different step sizes in each iteration and use a non-monotone step size criterion without any line search allowing them to work adaptively. The strong convergence of the iterative sequences formed by the proposed algorithms is established under some mild conditions. Several numerical experiments occurring in finite- and infinite-dimensional Hilbert spaces and applications to optimal control problems as well as signal processing problems are given. Performance profiles are used to verify the computational efficiency and advantages of the proposed algorithms with respect to some known ones.},\\nkeywords={Variational inequality problem,  Inertial method,  Projection and contraction method,  Subgradient extragradient method, Pseudomonotone operator, Optimal control problem, Signal processing problem, Strong convergence},\\nabbrev_source_title={Optimization},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Li, S.\"],\"key\":\"TL_OPT22\",\"id\":\"TL_OPT22\",\"bibbaseid\":\"tan-li-modifiedinertialprojectionandcontractionalgorithmswithnonmonotonicstepsizesforsolvingvariationalinequalitiesandtheirapplications-2022\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TL-OPT2022.pdf\"},\"keyword\":[\"Variational inequality problem\",\"Inertial method\",\"Projection and contraction method\",\"Subgradient extragradient method\",\"Pseudomonotone operator\",\"Optimal control problem\",\"Signal processing problem\",\"Strong convergence\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Li\"],\"firstnames\":[\"Songxiao\"],\"suffixes\":[]}],\"title\":\"Revisiting projection and contraction algorithms for solving variational inequalities and applications\",\"journal\":\"Applied Set-Valued Analysis and Optimization\",\"year\":\"2022\",\"volume\":\"4\",\"number\":\"2\",\"pages\":\"167–183\",\"doi\":\"10.23952/asvao.4.2022.2.03\",\"url\":\"https://bingtan.me/files/paper/TL-ASVAO2022.pdf\",\"abstract\":\"We provide two novel projection and contraction algorithms to find the minimum-norm solution of the variational inequality problem with a pseudo monotone and non-Lipschitz continuous operator in a real Hilbert space. Our algorithms can work adaptively without requiring the prior information of the Lipschitz constant of the operator. Strong convergence theorems for the suggested iterative algorithms are established under suitable conditions. Some numerical experiments are discussed to demonstrate the computational efficiency of the proposed algorithms in comparison with several existing ones.\",\"keywords\":\"Variational inequality problem, Subgradient extragradient method, Projection and contraction method, Inertial method, Pseudomonotone operator\",\"abbrev_source_title\":\"Appl. Set-Valued Anal. Optim.\",\"bibtex\":\"@ARTICLE{TL_ASVAO22,\\nauthor={Tan, Bing and Li, Songxiao},\\ntitle={Revisiting projection and contraction algorithms for solving variational inequalities and applications},\\njournal={Applied Set-Valued Analysis and Optimization},\\nyear={2022},\\nvolume={4},\\nnumber={2},\\npages={167--183},\\ndoi={10.23952/asvao.4.2022.2.03},\\nurl={https://bingtan.me/files/paper/TL-ASVAO2022.pdf},\\nabstract={We provide two novel projection and contraction algorithms to find the minimum-norm solution of the variational inequality problem with a pseudo monotone and non-Lipschitz continuous operator in a real Hilbert space. Our algorithms can work adaptively without requiring the prior information of the Lipschitz constant of the operator. Strong convergence theorems for the suggested iterative algorithms are established under suitable conditions. Some numerical experiments are discussed to demonstrate the computational efficiency of the proposed algorithms in comparison with several existing ones.},\\nkeywords={Variational inequality problem, Subgradient extragradient method, Projection and contraction method, Inertial method, Pseudomonotone operator},\\nabbrev_source_title={Appl. Set-Valued Anal. Optim.},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Li, S.\"],\"key\":\"TL_ASVAO22\",\"id\":\"TL_ASVAO22\",\"bibbaseid\":\"tan-li-revisitingprojectionandcontractionalgorithmsforsolvingvariationalinequalitiesandapplications-2022\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TL-ASVAO2022.pdf\"},\"keyword\":[\"Variational inequality problem\",\"Subgradient extragradient method\",\"Projection and contraction method\",\"Inertial method\",\"Pseudomonotone operator\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Zhou\"],\"firstnames\":[\"Zheng\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Li\"],\"firstnames\":[\"Songxiao\"],\"suffixes\":[]}],\"title\":\"Viscosity-type inertial extragradient algorithms for solving variational inequality problems and fixed point problems\",\"journal\":\"Journal of Applied Mathematics and Computing\",\"year\":\"2022\",\"volume\":\"68\",\"number\":\"2\",\"pages\":\"1387–1411\",\"doi\":\"10.1007/s12190-021-01576-z\",\"url\":\"https://bingtan.me/files/paper/TZL-JAMC2022.pdf\",\"abstract\":\"The paper presents two inertial viscosity-type extragradient algorithms for finding a common solution of the variational inequality problem involving a monotone and Lipschitz continuous operator and of the fixed point problem with a demicontractive mapping in real Hilbert spaces. Our algorithms use a simple step size rule which is generated by some calculations at each iteration. Two strong convergence theorems are obtained without the prior knowledge of the Lipschitz constant of the operator. The numerical behaviors of the proposed algorithms in some numerical experiments are reported and compared with previously known ones.\",\"keywords\":\"Fixed point problem, Inertial method, Subgradient extragradient method, Tseng's extragradient method, Variational inequality problem\",\"abbrev_source_title\":\"J. Appl. Math. Comput.\",\"bibtex\":\"@ARTICLE{TZL_JAMC22,\\nauthor={Tan, Bing and Zhou, Zheng and Li, Songxiao},\\ntitle={Viscosity-type inertial extragradient algorithms for solving variational inequality problems and fixed point problems},\\njournal={Journal of Applied Mathematics and Computing},\\nyear={2022},\\nvolume={68},\\nnumber={2},\\npages={1387--1411},\\ndoi={10.1007/s12190-021-01576-z},\\nurl={https://bingtan.me/files/paper/TZL-JAMC2022.pdf},\\nabstract={The paper presents two inertial viscosity-type extragradient algorithms for finding a common solution of the variational inequality problem involving a monotone and Lipschitz continuous operator and of the fixed point problem with a demicontractive mapping in real Hilbert spaces. Our algorithms use a simple step size rule which is generated by some calculations at each iteration. Two strong convergence theorems are obtained without the prior knowledge of the Lipschitz constant of the operator. The numerical behaviors of the proposed algorithms in some numerical experiments are reported and compared with previously known ones.},\\nkeywords={Fixed point problem,  Inertial method,  Subgradient extragradient method,  Tseng's extragradient method,  Variational inequality problem},\\nabbrev_source_title={J. Appl. Math. Comput.},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Zhou, Z.\",\"Li, S.\"],\"key\":\"TZL_JAMC22\",\"id\":\"TZL_JAMC22\",\"bibbaseid\":\"tan-zhou-li-viscositytypeinertialextragradientalgorithmsforsolvingvariationalinequalityproblemsandfixedpointproblems-2022\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TZL-JAMC2022.pdf\"},\"keyword\":[\"Fixed point problem\",\"Inertial method\",\"Subgradient extragradient method\",\"Tseng's extragradient method\",\"Variational inequality problem\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Li\"],\"firstnames\":[\"Songxiao\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Cho\"],\"firstnames\":[\"Sun\",\"Y.\"],\"suffixes\":[]}],\"title\":\"Revisiting inertial subgradient extragradient algorithms for solving bilevel variational inequality problems\",\"journal\":\"Journal of Applied and Numerical Optimization\",\"year\":\"2022\",\"volume\":\"4\",\"number\":\"3\",\"pages\":\"425–444\",\"doi\":\"10.23952/jano.4.2022.3.08\",\"url\":\"https://bingtan.me/files/paper/TLC-JANO2022.pdf\",\"abstract\":\"In this paper, four modified subgradient extragradient algorithms are proposed for solving bilevel pseudomonotone variational inequality problems in real Hilbert spaces. The proposed algorithms can work adaptively without the prior knowledge of the Lipschitz constant of the pseudomonotone mapping. Strong convergence theorems for the suggested algorithms are established under suitable and mild conditions. Finally, some numerical experiments and applications are performed to verify the efficiency of the proposed algorithms with respect to some previously known ones.\",\"keywords\":\"Inertial method, Pseudomonotone operator, Subgradient extragradient method, Bilevel variational inequality problem\",\"abbrev_source_title\":\"J. Appl. Numer. Optim.\",\"bibtex\":\"@ARTICLE{TLC_JANO22,\\nauthor={Tan, Bing and Li, Songxiao and Cho, Sun Y.},\\ntitle={Revisiting inertial subgradient extragradient algorithms for solving bilevel variational inequality problems},\\njournal={Journal of Applied and Numerical Optimization},\\nyear={2022},\\nvolume={4},\\nnumber={3},\\npages={425--444},\\ndoi={10.23952/jano.4.2022.3.08},\\nurl={https://bingtan.me/files/paper/TLC-JANO2022.pdf},\\nabstract={In this paper, four modified subgradient extragradient algorithms are proposed for solving bilevel pseudomonotone variational inequality problems in real Hilbert spaces. The proposed algorithms can work adaptively without the prior knowledge of the Lipschitz constant of the pseudomonotone mapping. Strong convergence theorems for the suggested algorithms are established under suitable and mild conditions. Finally, some numerical experiments and applications are performed to verify the efficiency of the proposed algorithms with respect to some previously known ones.},\\nkeywords={Inertial method, Pseudomonotone operator, Subgradient extragradient method, Bilevel variational inequality problem},\\nabbrev_source_title={J. Appl. Numer. Optim.},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Li, S.\",\"Cho, S. Y.\"],\"key\":\"TLC_JANO22\",\"id\":\"TLC_JANO22\",\"bibbaseid\":\"tan-li-cho-revisitinginertialsubgradientextragradientalgorithmsforsolvingbilevelvariationalinequalityproblems-2022\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TLC-JANO2022.pdf\"},\"keyword\":[\"Inertial method\",\"Pseudomonotone operator\",\"Subgradient extragradient method\",\"Bilevel variational inequality problem\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"downloads\":1,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Cho\"],\"firstnames\":[\"Sun\",\"Y.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Yao\"],\"firstnames\":[\"Jen\",\"C.\"],\"suffixes\":[]}],\"title\":\"Accelerated inertial subgradient extragradient algorithms with non-monotonic step sizes for equilibrium problems and fixed point problems\",\"journal\":\"Journal of Nonlinear and Variational Analysis\",\"year\":\"2022\",\"volume\":\"6\",\"number\":\"1\",\"pages\":\"89–122\",\"doi\":\"10.23952/jnva.6.2022.1.06\",\"url\":\"https://bingtan.me/files/paper/TCY-JNVA2022.pdf\",\"abstract\":\"This paper introduces several new accelerated subgradient extragradient methods with inertial effects for approximating a solution of a pseudomonotone equilibrium problem and a fixed point problem involving a quasi-nonexpansive mapping or a demicontractive mapping in real Hilbert spaces. The proposed algorithms use an adaptive non-monotonic step size criterion that does not include any Armijo line search process. Strong convergence theorems of the suggested iterative algorithms are established without the prior knowledge of the Lipschitz constants of the bifunction. Moreover, $R$-linear convergence is guaranteed under the assumption that the bifunction satisfies strong pseudomonotonicity. Applications to variational inequality problems are also considered. Finally, some numerical examples and applications, which demonstrate the advantages and efficiency of the proposed algorithms, are given.\",\"keywords\":\"Equilibrium problem, Fixed point problem, Inertial method, Pseudomonotone bifunction, Subgradient extragradient method\",\"abbrev_source_title\":\"J. Nonlinear Var. Anal.\",\"bibtex\":\"@ARTICLE{TCY_JNVA22,\\nauthor={Tan, Bing and Cho, Sun Y. and Yao, Jen C.},\\ntitle={Accelerated inertial subgradient extragradient algorithms with non-monotonic step sizes for equilibrium problems and fixed point problems},\\njournal={Journal of Nonlinear and Variational Analysis},\\nyear={2022},\\nvolume={6},\\nnumber={1},\\npages={89--122},\\ndoi={10.23952/jnva.6.2022.1.06},\\nurl={https://bingtan.me/files/paper/TCY-JNVA2022.pdf},\\nabstract={This paper introduces several new accelerated subgradient extragradient methods with inertial effects for approximating a solution of a pseudomonotone equilibrium problem and a fixed point problem involving a quasi-nonexpansive mapping or a demicontractive mapping in real Hilbert spaces. The proposed algorithms use an adaptive non-monotonic step size criterion that does not include any Armijo line search process. Strong convergence theorems of the suggested iterative algorithms are established without the prior knowledge of the Lipschitz constants of the bifunction. Moreover, $R$-linear convergence is guaranteed under the assumption that the bifunction satisfies strong pseudomonotonicity. Applications to variational inequality problems are also considered. Finally, some numerical examples and applications, which demonstrate the advantages and efficiency of the proposed algorithms, are given.},\\nkeywords={Equilibrium problem,  Fixed point problem,  Inertial method,  Pseudomonotone bifunction,  Subgradient extragradient method},\\nabbrev_source_title={J. Nonlinear Var. Anal.},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Cho, S. Y.\",\"Yao, J. C.\"],\"key\":\"TCY_JNVA22\",\"id\":\"TCY_JNVA22\",\"bibbaseid\":\"tan-cho-yao-acceleratedinertialsubgradientextragradientalgorithmswithnonmonotonicstepsizesforequilibriumproblemsandfixedpointproblems-2022\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TCY-JNVA2022.pdf\"},\"keyword\":[\"Equilibrium problem\",\"Fixed point problem\",\"Inertial method\",\"Pseudomonotone bifunction\",\"Subgradient extragradient method\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Cho\"],\"firstnames\":[\"Sun\",\"Y.\"],\"suffixes\":[]}],\"title\":\"Two adaptive modified subgradient extragradient methods for bilevel pseudomonotone variational inequalities with applications\",\"journal\":\"Communications in Nonlinear Science and Numerical Simulation\",\"year\":\"2022\",\"volume\":\"107\",\"doi\":\"10.1016/j.cnsns.2021.106160\",\"pages\":\"106160\",\"url\":\"https://bingtan.me/files/paper/TC-CNSNS2022.pdf\",\"abstract\":\"We consider the bilevel variational inequality problem with a pseudomonotone operator in real Hilbert spaces and investigate two modified subgradient extragradient methods with inertial terms. Our first scheme requires the operator to be Lipschitz continuous (the Lipschitz constant does not need to be known) while the second one only requires it to be uniformly continuous. The proposed methods employ two adaptive stepsizes making them work without the prior knowledge of the Lipschitz constant of the mapping. The strong convergence properties of the iterative sequences generated by the proposed algorithms are obtained under mild conditions. Some numerical tests and applications are given to demonstrate the advantages and efficiency of the stated schemes over previously known ones.\",\"keywords\":\"Adaptive stepsize, Bilevel variational inequality problem, Extragradient method, Inertial method, Pseudomonotone operator\",\"abbrev_source_title\":\"Comm. Nonlinear Sci. Numer. Simul.\",\"bibtex\":\"@ARTICLE{TC_CNSNS22,\\nauthor={Tan, Bing and Cho, Sun Y.},\\ntitle={Two adaptive modified subgradient extragradient methods for bilevel pseudomonotone variational inequalities with applications},\\njournal={Communications in Nonlinear Science and Numerical Simulation},\\nyear={2022},\\nvolume={107},\\ndoi={10.1016/j.cnsns.2021.106160},\\npages={106160},\\nurl={https://bingtan.me/files/paper/TC-CNSNS2022.pdf},\\nabstract={We consider the bilevel variational inequality problem with a pseudomonotone operator in real Hilbert spaces and investigate two modified subgradient extragradient methods with inertial terms. Our first scheme requires the operator to be Lipschitz continuous (the Lipschitz constant does not need to be known) while the second one only requires it to be uniformly continuous. The proposed methods employ two adaptive stepsizes making them work without the prior knowledge of the Lipschitz constant of the mapping. The strong convergence properties of the iterative sequences generated by the proposed algorithms are obtained under mild conditions. Some numerical tests and applications are given to demonstrate the advantages and efficiency of the stated schemes over previously known ones.},\\nkeywords={Adaptive stepsize,  Bilevel variational inequality problem,  Extragradient method,  Inertial method,  Pseudomonotone operator},\\nabbrev_source_title={Comm. Nonlinear Sci. Numer. Simul.},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Cho, S. Y.\"],\"key\":\"TC_CNSNS22\",\"id\":\"TC_CNSNS22\",\"bibbaseid\":\"tan-cho-twoadaptivemodifiedsubgradientextragradientmethodsforbilevelpseudomonotonevariationalinequalitieswithapplications-2022\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TC-CNSNS2022.pdf\"},\"keyword\":[\"Adaptive stepsize\",\"Bilevel variational inequality problem\",\"Extragradient method\",\"Inertial method\",\"Pseudomonotone operator\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Cho\"],\"firstnames\":[\"Sun\",\"Y.\"],\"suffixes\":[]}],\"title\":\"Two projection-based methods for bilevel pseudomonotone variational inequalities involving non-Lipschitz operators\",\"journal\":\"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas\",\"year\":\"2022\",\"volume\":\"116\",\"number\":\"2\",\"doi\":\"10.1007/s13398-021-01205-1\",\"pages\":\"64\",\"url\":\"https://bingtan.me/files/paper/TC-RACSAM2022.pdf\",\"abstract\":\"In this paper, we propose two new iterative algorithms to discover solutions of bilevel pseudomonotone variational inequalities with non-Lipschitz continuous operators in real Hilbert spaces. Our proposed algorithms need to compute the projection on the feasible set only once in each iteration although they employ Armijo line search methods. Strong convergence theorems of the suggested algorithms are established under suitable and weaker conditions. Some numerical experiments and applications are given to demonstrate the performance of the offered algorithms compared to some known ones.\",\"keywords\":\"Armijo stepsize, Bilevel variational inequality problem, Inertial method, Non-Lipschitz operator, Pseudomonotone operator\",\"abbrev_source_title\":\"Rev. R. Acad. Cienc. Exactas F ́is. Nat. Ser. A Mat. RACSAM\",\"bibtex\":\"@ARTICLE{TC_RCSM22,\\nauthor={Tan, Bing and Cho, Sun Y.},\\ntitle={Two projection-based methods for bilevel pseudomonotone variational inequalities involving non-Lipschitz operators},\\njournal={Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas},\\nyear={2022},\\nvolume={116},\\nnumber={2},\\ndoi={10.1007/s13398-021-01205-1},\\npages={64},\\nurl={https://bingtan.me/files/paper/TC-RACSAM2022.pdf},\\nabstract={In this paper, we propose two new iterative algorithms to discover solutions of bilevel pseudomonotone variational inequalities with non-Lipschitz continuous operators in real Hilbert spaces. Our proposed algorithms need to compute the projection on the feasible set only once in each iteration although they employ Armijo line search methods. Strong convergence theorems of the suggested algorithms are established under suitable and weaker conditions. Some numerical experiments and applications are given to demonstrate the performance of the offered algorithms compared to some known ones.},\\nkeywords={Armijo stepsize,  Bilevel variational inequality problem,  Inertial method,  Non-Lipschitz operator,  Pseudomonotone operator},\\nabbrev_source_title={Rev. R. Acad. Cienc. Exactas F{\\\\' i}s. Nat. Ser. A Mat. RACSAM},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Cho, S. Y.\"],\"key\":\"TC_RCSM22\",\"id\":\"TC_RCSM22\",\"bibbaseid\":\"tan-cho-twoprojectionbasedmethodsforbilevelpseudomonotonevariationalinequalitiesinvolvingnonlipschitzoperators-2022\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TC-RACSAM2022.pdf\"},\"keyword\":[\"Armijo stepsize\",\"Bilevel variational inequality problem\",\"Inertial method\",\"Non-Lipschitz operator\",\"Pseudomonotone operator\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Cho\"],\"firstnames\":[\"Sun\",\"Y.\"],\"suffixes\":[]}],\"title\":\"Strong convergence of inertial forward-backward methods for solving monotone inclusions\",\"journal\":\"Applicable Analysis\",\"year\":\"2022\",\"volume\":\"101\",\"number\":\"15\",\"pages\":\"5386–5414\",\"doi\":\"10.1080/00036811.2021.1892080\",\"url\":\"https://bingtan.me/files/paper/TC-AA2022.pdf\",\"abstract\":\"The paper presents four modifications of the inertial forward–backward splitting method for monotone inclusion problems in the framework of real Hilbert spaces. The advantages of our iterative schemes are that the single-valued operator is Lipschitz continuous monotone rather than cocoercive and the Lipschitz constant does not require to be known. The strong convergence of the suggested approaches is obtained under some standard and mild conditions. Finally, several numerical experiments in finite- and infinite-dimensional spaces are proposed to demonstrate the advantages of our algorithms over the existing related ones.\",\"keywords\":\"Inclusion problem, Inertial forward–backward method, Projection and contraction method, Tseng's extragradient method, Viscosity method, Signal processing problem\",\"abbrev_source_title\":\"Appl. Anal.\",\"bibbase_note\":\"<span style=\\\"color: red\\\">(ESI Highly Cited Paper)</span>\",\"bibtex\":\"@ARTICLE{TC_AA22,\\nauthor={Tan, Bing and Cho, Sun Y.},\\ntitle={Strong convergence of inertial forward-backward methods for solving monotone inclusions},\\njournal={Applicable Analysis},\\nyear={2022},\\nvolume={101},\\nnumber={15},\\npages={5386--5414},\\ndoi={10.1080/00036811.2021.1892080},\\nurl={https://bingtan.me/files/paper/TC-AA2022.pdf},\\nabstract={The paper presents four modifications of the inertial forward–backward splitting method for monotone inclusion problems in the framework of real Hilbert spaces. The advantages of our iterative schemes are that the single-valued operator is Lipschitz continuous monotone rather than cocoercive and the Lipschitz constant does not require to be known. The strong convergence of the suggested approaches is obtained under some standard and mild conditions. Finally, several numerical experiments in finite- and infinite-dimensional spaces are proposed to demonstrate the advantages of our algorithms over the existing related ones.},\\nkeywords={Inclusion problem,  Inertial forward–backward method,  Projection and contraction method,  Tseng's extragradient method,  Viscosity method, Signal processing problem},\\nabbrev_source_title={Appl. Anal.},\\nbibbase_note={<span style=\\\"color: red\\\">(ESI Highly Cited Paper)</span>},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Cho, S. Y.\"],\"key\":\"TC_AA22\",\"id\":\"TC_AA22\",\"bibbaseid\":\"tan-cho-strongconvergenceofinertialforwardbackwardmethodsforsolvingmonotoneinclusions-2022\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TC-AA2022.pdf\"},\"keyword\":[\"Inclusion problem\",\"Inertial forward–backward method\",\"Projection and contraction method\",\"Tseng's extragradient method\",\"Viscosity method\",\"Signal processing problem\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Cho\"],\"firstnames\":[\"Sun\",\"Y.\"],\"suffixes\":[]}],\"title\":\"Inertial extragradient algorithms with non-monotone stepsizes for pseudomonotone variational inequalities and applications\",\"journal\":\"Computational and Applied Mathematics\",\"year\":\"2022\",\"volume\":\"41\",\"number\":\"3\",\"doi\":\"10.1007/s40314-022-01819-0\",\"pages\":\"121\",\"url\":\"https://bingtan.me/files/paper/TC-COAM2022.pdf\",\"abstract\":\"The goal of this paper is to construct several fast iterative algorithms for solving pseudomonotone variational inequalities in real Hilbert spaces. We introduce two extragradient algorithms with inertial terms and give a strong convergence analysis under suitable assumptions. The suggested algorithms need to compute the projection on the feasible set only once in each iteration and can update the step size adaptively without any line search condition. Some numerical experiments and applications are implemented to illustrate the advantages and efficiency of the suggested algorithms over the related known methods.\",\"keywords\":\"Inertial method, Pseudomonotone operator, Subgradient extragradient method, Tseng's extragradient method, Variational inequality problem\",\"abbrev_source_title\":\"Comput. Appl. Math.\",\"bibtex\":\"@ARTICLE{TC_COAM22,\\nauthor={Tan, Bing and Cho, Sun Y.},\\ntitle={Inertial extragradient algorithms with non-monotone stepsizes for pseudomonotone variational inequalities and applications},\\njournal={Computational and Applied Mathematics},\\nyear={2022},\\nvolume={41},\\nnumber={3},\\ndoi={10.1007/s40314-022-01819-0},\\npages={121},\\nurl={https://bingtan.me/files/paper/TC-COAM2022.pdf},\\nabstract={The goal of this paper is to construct several fast iterative algorithms for solving pseudomonotone variational inequalities in real Hilbert spaces. We introduce two extragradient algorithms with inertial terms and give a strong convergence analysis under suitable assumptions. The suggested algorithms need to compute the projection on the feasible set only once in each iteration and can update the step size adaptively without any line search condition. Some numerical experiments and applications are implemented to illustrate the advantages and efficiency of the suggested algorithms over the related known methods.},\\nkeywords={Inertial method,  Pseudomonotone operator,  Subgradient extragradient method,  Tseng's extragradient method,  Variational inequality problem},\\nabbrev_source_title={Comput. Appl. Math.},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Cho, S. Y.\"],\"key\":\"TC_COAM22\",\"id\":\"TC_COAM22\",\"bibbaseid\":\"tan-cho-inertialextragradientalgorithmswithnonmonotonestepsizesforpseudomonotonevariationalinequalitiesandapplications-2022\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TC-COAM2022.pdf\"},\"keyword\":[\"Inertial method\",\"Pseudomonotone operator\",\"Subgradient extragradient method\",\"Tseng's extragradient method\",\"Variational inequality problem\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Cho\"],\"firstnames\":[\"Sun\",\"Y.\"],\"suffixes\":[]}],\"title\":\"Two new projection algorithms for variational inequalities in Hilbert spaces\",\"journal\":\"Journal of Nonlinear and Convex Analysis\",\"year\":\"2022\",\"volume\":\"23\",\"number\":\"11\",\"pages\":\"2523–2534\",\"url\":\"https://bingtan.me/files/paper/TC-JNCA2022.pdf\",\"abstract\":\"In this paper, two new projection-type algorithms are introduced for solving pseudomonotone variational inequalities in real Hilbert spaces. The proposed methods use two non-monotonic step sizes allowing them to work adaptively without the prior information of the Lipschitz constant of the operator. Strong convergence theorems for the proposed methods are established under suitable conditions. A fundamental numerical example is given to verify the efficiency of the suggested methods in comparison with some known ones.\",\"keywords\":\"Inertial method, Pseudomonotone operator, Variational inequality problem, Projection method\",\"abbrev_source_title\":\"J. Nonlinear Convex Anal.\",\"bibtex\":\"@ARTICLE{TC_JNCA22,\\nauthor={Tan, Bing and Cho, Sun Y.},\\ntitle={Two new projection algorithms for variational inequalities in Hilbert spaces},\\njournal={Journal of Nonlinear and Convex Analysis},\\nyear={2022},\\nvolume={23},\\nnumber={11},\\npages={2523--2534},\\nurl={https://bingtan.me/files/paper/TC-JNCA2022.pdf},\\nabstract={In this paper, two new projection-type algorithms are introduced for solving pseudomonotone variational inequalities in real Hilbert spaces. The proposed methods use two non-monotonic step sizes allowing them to work adaptively without the prior information of the Lipschitz constant of the operator. Strong convergence theorems for the proposed methods are established under suitable conditions. A fundamental numerical example is given to verify the efficiency of the suggested methods in comparison with some known ones.},\\nkeywords={Inertial method, Pseudomonotone operator,  Variational inequality problem, Projection method},\\nabbrev_source_title={J. Nonlinear Convex Anal.},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Cho, S. Y.\"],\"key\":\"TC_JNCA22\",\"id\":\"TC_JNCA22\",\"bibbaseid\":\"tan-cho-twonewprojectionalgorithmsforvariationalinequalitiesinhilbertspaces-2022\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TC-JNCA2022.pdf\"},\"keyword\":[\"Inertial method\",\"Pseudomonotone operator\",\"Variational inequality problem\",\"Projection method\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Zhou\"],\"firstnames\":[\"Zheng\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Li\"],\"firstnames\":[\"Songxiao\"],\"suffixes\":[]}],\"title\":\"Adaptive hybrid steepest descent algorithms involving an inertial extrapolation term for split monotone variational inclusion problems\",\"journal\":\"Mathematical Methods in the Applied Sciences\",\"year\":\"2022\",\"volume\":\"45\",\"number\":\"15\",\"pages\":\"8835–8853\",\"doi\":\"10.1002/mma.7931\",\"url\":\"https://bingtan.me/files/paper/ZTL-MMAS2022.pdf\",\"abstract\":\"In this paper, we discuss the split monotone variational inclusion problem and propose two new inertial algorithms in infinite-dimensional Hilbert spaces. The iterative sequence by the proposed algorithms converges strongly to the solution of a certain variational inequality with the help of the hybrid steepest descent method. Furthermore, an adaptive step size criterion is considered in suggested algorithms to avoid the difficulty of calculating the operator norm. Meanwhile, our results are also applied to several other types of split problems. Finally, some numerical experiments show that our algorithms are realistic and summarize the known results.\",\"keywords\":\"Adaptive stepsize, Hybrid steepest descent method, Inertial method, Signal processing problem, Strong convergence\",\"abbrev_source_title\":\"Math. Methods Appl. Sci.\",\"bibtex\":\"@ARTICLE{ZTL_MMAS22,\\nauthor={Zhou, Zheng and Tan, Bing and Li, Songxiao},\\ntitle={Adaptive hybrid steepest descent algorithms involving an inertial extrapolation term for split monotone variational inclusion problems},\\njournal={Mathematical Methods in the Applied Sciences},\\nyear={2022},\\nvolume={45},\\nnumber={15},\\npages={8835--8853},\\ndoi={10.1002/mma.7931},\\nurl={https://bingtan.me/files/paper/ZTL-MMAS2022.pdf},\\nabstract={In this paper, we discuss the split monotone variational inclusion problem and propose two new inertial algorithms in infinite-dimensional Hilbert spaces. The iterative sequence by the proposed algorithms converges strongly to the solution of a certain variational inequality with the help of the hybrid steepest descent method. Furthermore, an adaptive step size criterion is considered in suggested algorithms to avoid the difficulty of calculating the operator norm. Meanwhile, our results are also applied to several other types of split problems. Finally, some numerical experiments show that our algorithms are realistic and summarize the known results.},\\nkeywords={Adaptive stepsize,  Hybrid steepest descent method,  Inertial method,  Signal processing problem,  Strong convergence},\\nabbrev_source_title={Math. Methods Appl. Sci.},\\n}\\n\\n\",\"author_short\":[\"Zhou, Z.\",\"Tan, B.\",\"Li, S.\"],\"key\":\"ZTL_MMAS22\",\"id\":\"ZTL_MMAS22\",\"bibbaseid\":\"zhou-tan-li-adaptivehybridsteepestdescentalgorithmsinvolvinganinertialextrapolationtermforsplitmonotonevariationalinclusionproblems-2022\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/ZTL-MMAS2022.pdf\"},\"keyword\":[\"Adaptive stepsize\",\"Hybrid steepest descent method\",\"Inertial method\",\"Signal processing problem\",\"Strong convergence\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"downloads\":1,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Zhou\"],\"firstnames\":[\"Zheng\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Cho\"],\"firstnames\":[\"Sun\",\"Y.\"],\"suffixes\":[]}],\"title\":\"Alternated inertial subgradient extragradient methods for solving variational inequalities\",\"journal\":\"Journal of Nonlinear and Convex Analysis\",\"year\":\"2022\",\"volume\":\"23\",\"number\":\"11\",\"pages\":\"2593–2604\",\"url\":\"https://bingtan.me/files/paper/ZTC-JNCA2022.pdf\",\"abstract\":\"The goal of this paper is to study some iterative algorithms for solving a pseudomonotone variational inequality in Hilbert spaces. The iterative algorithms presented in this paper are based on the alternated inertial method and the subgradient extragradient method. Weak convergence of the algorithms is established by the adaptive stepsize criterion in Hilbert spaces.\",\"keywords\":\"Alternated inertial method, Pseudomonotone operator, Variational inequality problem, Subgradient extragradient method\",\"abbrev_source_title\":\"J. Nonlinear Convex Anal.\",\"bibtex\":\"@ARTICLE{ZTC_JNCA22,\\nauthor={Zhou, Zheng and Tan, Bing and Cho, Sun Y.},\\ntitle={Alternated inertial subgradient extragradient methods for solving variational inequalities},\\njournal={Journal of Nonlinear and Convex Analysis},\\nyear={2022},\\nvolume={23},\\nnumber={11},\\npages={2593--2604},\\nurl={https://bingtan.me/files/paper/ZTC-JNCA2022.pdf},\\nabstract={The goal of this paper is to study some iterative algorithms for solving a pseudomonotone variational inequality in Hilbert spaces. The iterative algorithms presented in this paper are based on the alternated inertial method and the subgradient extragradient method. Weak convergence of the algorithms is established by the adaptive stepsize criterion in Hilbert spaces.},\\nkeywords={Alternated inertial method, Pseudomonotone operator,  Variational inequality problem, Subgradient extragradient method},\\nabbrev_source_title={J. Nonlinear Convex Anal.},\\n}\\n\\n\",\"author_short\":[\"Zhou, Z.\",\"Tan, B.\",\"Cho, S. Y.\"],\"key\":\"ZTC_JNCA22\",\"id\":\"ZTC_JNCA22\",\"bibbaseid\":\"zhou-tan-cho-alternatedinertialsubgradientextragradientmethodsforsolvingvariationalinequalities-2022\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/ZTC-JNCA2022.pdf\"},\"keyword\":[\"Alternated inertial method\",\"Pseudomonotone operator\",\"Variational inequality problem\",\"Subgradient extragradient method\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Zhou\"],\"firstnames\":[\"Zheng\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Li\"],\"firstnames\":[\"Songxiao\"],\"suffixes\":[]}],\"title\":\"Two self-adaptive inertial projection algorithms for solving split variational inclusion problems\",\"journal\":\"AIMS Mathematics\",\"year\":\"2022\",\"volume\":\"7\",\"number\":\"4\",\"pages\":\"4960–4973\",\"doi\":\"10.3934/math.2022276\",\"url\":\"https://bingtan.me/files/paper/ZTL-AIMS2022.pdf\",\"abstract\":\"This paper is to analyze the approximation solution of a split variational inclusion problem in the framework of Hilbert spaces. For this purpose, inertial hybrid and shrinking projection algorithms are proposed under the effect of a self-adaptive stepsize which does not require information of the norms of the given operators. The strong convergence properties of the proposed algorithms are obtained under mild constraints. Finally, a numerical experiment is given to illustrate the performance of proposed methods and to compare our algorithms with an existing algorithm.\",\"keywords\":\"Inertial method, Adaptive stepsize, Split variational inclusion problem\",\"abbrev_source_title\":\"AIMS Math.\",\"bibtex\":\"@ARTICLE{ZTL_AIMS22,\\nauthor={Zhou, Zheng and Tan, Bing and Li, Songxiao},\\ntitle={Two self-adaptive inertial projection algorithms for solving split variational inclusion problems},\\njournal={AIMS Mathematics},\\nyear={2022},\\nvolume={7},\\nnumber={4},\\npages={4960--4973},\\ndoi={10.3934/math.2022276},\\nurl={https://bingtan.me/files/paper/ZTL-AIMS2022.pdf},\\nabstract={This paper is to analyze the approximation solution of a split variational inclusion problem in the framework of Hilbert spaces. For this purpose, inertial hybrid and shrinking projection algorithms are proposed under the effect of a self-adaptive stepsize which does not require information of the norms of the given operators. The strong convergence properties of the proposed algorithms are obtained under mild constraints. Finally, a numerical experiment is given to illustrate the performance of proposed methods and to compare our algorithms with an existing algorithm.},\\nkeywords={Inertial method,  Adaptive stepsize,  Split variational inclusion problem},\\nabbrev_source_title={AIMS Math.},\\n}\\n\\n\",\"author_short\":[\"Zhou, Z.\",\"Tan, B.\",\"Li, S.\"],\"key\":\"ZTL_AIMS22\",\"id\":\"ZTL_AIMS22\",\"bibbaseid\":\"zhou-tan-li-twoselfadaptiveinertialprojectionalgorithmsforsolvingsplitvariationalinclusionproblems-2022\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/ZTL-AIMS2022.pdf\"},\"keyword\":[\"Inertial method\",\"Adaptive stepsize\",\"Split variational inclusion problem\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Fan\"],\"firstnames\":[\"Jingjing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Qin\"],\"firstnames\":[\"Xiaolong\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]}],\"title\":\"Tseng's extragradient algorithm for pseudomonotone variational inequalities on Hadamard manifolds\",\"journal\":\"Applicable Analysis\",\"year\":\"2022\",\"volume\":\"101\",\"number\":\"6\",\"pages\":\"2372–2385\",\"doi\":\"10.1080/00036811.2020.1807012\",\"url\":\"https://bingtan.me/files/paper/FQT-AA2022.pdf\",\"abstract\":\"In this paper, we investigate the Tseng's extragradient algorithm for non-Lipschitzian variational inequalities with pseudomonotone vector fields on Hadamard manifolds. The convergence analysis of the proposed algorithm is discussed under mild assumptions. Two experiments are provided to illustrate the asymptotical behavior of the algorithm. The results presented in this paper generalize some known results presented in the literature.\",\"keywords\":\"Extragradient method, Hadamard manifolds, Non-Lipschitz operator, Pseudomonotone vector field, Variational inequality problem\",\"abbrev_source_title\":\"Appl. Anal.\",\"bibtex\":\"@ARTICLE{FQT_AA22,\\nauthor={Fan, Jingjing and Qin, Xiaolong and Tan, Bing},\\ntitle={Tseng's extragradient algorithm for pseudomonotone variational inequalities on {H}adamard manifolds},\\njournal={Applicable Analysis},\\nyear={2022},\\nvolume={101},\\nnumber={6},\\npages={2372--2385},\\ndoi={10.1080/00036811.2020.1807012},\\nurl={https://bingtan.me/files/paper/FQT-AA2022.pdf},\\nabstract={In this paper, we investigate the Tseng's extragradient algorithm for non-Lipschitzian variational inequalities with pseudomonotone vector fields on Hadamard manifolds. The convergence analysis of the proposed algorithm is discussed under mild assumptions. Two experiments are provided to illustrate the asymptotical behavior of the algorithm. The results presented in this paper generalize some known results presented in the literature.},\\nkeywords={Extragradient method,  Hadamard manifolds,  Non-Lipschitz operator,  Pseudomonotone vector field,  Variational inequality problem},\\nabbrev_source_title={Appl. Anal.},\\n}\\n\\n\",\"author_short\":[\"Fan, J.\",\"Qin, X.\",\"Tan, B.\"],\"key\":\"FQT_AA22\",\"id\":\"FQT_AA22\",\"bibbaseid\":\"fan-qin-tan-tsengsextragradientalgorithmforpseudomonotonevariationalinequalitiesonhadamardmanifolds-2022\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/FQT-AA2022.pdf\"},\"keyword\":[\"Extragradient method\",\"Hadamard manifolds\",\"Non-Lipschitz operator\",\"Pseudomonotone vector field\",\"Variational inequality problem\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Qin\"],\"firstnames\":[\"Xiaolong\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Yao\"],\"firstnames\":[\"Jen\",\"C.\"],\"suffixes\":[]}],\"title\":\"Strong convergence of self-adaptive inertial algorithms for solving split variational inclusion problems with applications\",\"journal\":\"Journal of Scientific Computing\",\"year\":\"2021\",\"volume\":\"87\",\"number\":\"1\",\"doi\":\"10.1007/s10915-021-01428-9\",\"pages\":\"20\",\"url\":\"https://bingtan.me/files/paper/TQY-JSC2021.pdf\",\"abstract\":\"In this paper, four self-adaptive iterative algorithms with inertial effects are introduced to solve a split variational inclusion problem in real Hilbert spaces. One of the advantages of the suggested algorithms is that they can work without knowing the prior information of the operator norm. Strong convergence theorems of these algorithms are established under mild and standard assumptions. As applications, the split feasibility problem and the split minimization problem in real Hilbert spaces are studied. Finally, several preliminary numerical experiments as well as an example in the field of compressed sensing are proposed to support the advantages and efficiency of the suggested methods over some existing ones.\",\"keywords\":\"Inertial method, Mann method, Signal processing problem, Split variational inclusion problem, Strong convergence, Viscosity method\",\"abbrev_source_title\":\"J. Sci. Comput.\",\"bibbase_note\":\"<span style=\\\"color: red\\\">(ESI Highly Cited Paper)</span>\",\"bibtex\":\"@ARTICLE{TQY_JSC21,\\nauthor={Tan, Bing and Qin, Xiaolong and Yao, Jen C.},\\ntitle={Strong convergence of self-adaptive inertial algorithms for solving split variational inclusion problems with applications},\\njournal={Journal of Scientific Computing},\\nyear={2021},\\nvolume={87},\\nnumber={1},\\ndoi={10.1007/s10915-021-01428-9},\\npages={20},\\nurl={https://bingtan.me/files/paper/TQY-JSC2021.pdf},\\nabstract={In this paper, four self-adaptive iterative algorithms with inertial effects are introduced to solve a split variational inclusion problem in real Hilbert spaces. One of the advantages of the suggested algorithms is that they can work without knowing the prior information of the operator norm. Strong convergence theorems of these algorithms are established under mild and standard assumptions. As applications, the split feasibility problem and the split minimization problem in real Hilbert spaces are studied. Finally, several preliminary numerical experiments as well as an example in the field of compressed sensing are proposed to support the advantages and efficiency of the suggested methods over some existing ones.},\\nkeywords={Inertial method,  Mann method,  Signal processing problem,  Split variational inclusion problem,  Strong convergence,  Viscosity method},\\nabbrev_source_title={J. Sci. Comput.},\\nbibbase_note={<span style=\\\"color: red\\\">(ESI Highly Cited Paper)</span>},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Qin, X.\",\"Yao, J. C.\"],\"key\":\"TQY_JSC21\",\"id\":\"TQY_JSC21\",\"bibbaseid\":\"tan-qin-yao-strongconvergenceofselfadaptiveinertialalgorithmsforsolvingsplitvariationalinclusionproblemswithapplications-2021\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TQY-JSC2021.pdf\"},\"keyword\":[\"Inertial method\",\"Mann method\",\"Signal processing problem\",\"Split variational inclusion problem\",\"Strong convergence\",\"Viscosity method\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Qin\"],\"firstnames\":[\"Xiaolong\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Yao\"],\"firstnames\":[\"Jen\",\"C.\"],\"suffixes\":[]}],\"title\":\"Two modified inertial projection algorithms for bilevel pseudomonotone variational inequalities with applications to optimal control problems\",\"journal\":\"Numerical Algorithms\",\"year\":\"2021\",\"volume\":\"88\",\"number\":\"4\",\"pages\":\"1757–1786\",\"doi\":\"10.1007/s11075-021-01093-x\",\"url\":\"https://bingtan.me/files/paper/TQY-NUMA2021.pdf\",\"abstract\":\"In this paper, we investigate two new algorithms for solving bilevel pseudomonotone variational inequality problems in real Hilbert spaces. The advantages of our algorithms are that they only need to calculate one projection on the feasible set in each iteration, and do not require the prior information of the Lipschitz constant of the cost operator. Furthermore, two new algorithms are derived to solve variational inequality problems. We establish the strong convergence of the proposed algorithms under some suitable conditions imposed on parameters. Finally, several numerical results and applications in optimal control problems are reported to illustrate the efficiency and advantages of the proposed algorithms.\",\"keywords\":\"Bilevel variational inequality problem, Hybrid steepest descent method, Inertial extragradient method, Projection and contraction method, Pseudomonotone operator\",\"abbrev_source_title\":\"Numer. Algorithms\",\"bibtex\":\"@ARTICLE{TQY_NUMA21,\\nauthor={Tan, Bing and Qin, Xiaolong and Yao, Jen C.},\\ntitle={Two modified inertial projection algorithms for bilevel pseudomonotone variational inequalities with applications to optimal control problems},\\njournal={Numerical Algorithms},\\nyear={2021},\\nvolume={88},\\nnumber={4},\\npages={1757--1786},\\ndoi={10.1007/s11075-021-01093-x},\\nurl={https://bingtan.me/files/paper/TQY-NUMA2021.pdf},\\nabstract={In this paper, we investigate two new algorithms for solving bilevel pseudomonotone variational inequality problems in real Hilbert spaces. The advantages of our algorithms are that they only need to calculate one projection on the feasible set in each iteration, and do not require the prior information of the Lipschitz constant of the cost operator. Furthermore, two new algorithms are derived to solve variational inequality problems. We establish the strong convergence of the proposed algorithms under some suitable conditions imposed on parameters. Finally, several numerical results and applications in optimal control problems are reported to illustrate the efficiency and advantages of the proposed algorithms.},\\nkeywords={Bilevel variational inequality problem,  Hybrid steepest descent method,  Inertial extragradient method,  Projection and contraction method,  Pseudomonotone operator},\\nabbrev_source_title={Numer. Algorithms},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Qin, X.\",\"Yao, J. C.\"],\"key\":\"TQY_NUMA21\",\"id\":\"TQY_NUMA21\",\"bibbaseid\":\"tan-qin-yao-twomodifiedinertialprojectionalgorithmsforbilevelpseudomonotonevariationalinequalitieswithapplicationstooptimalcontrolproblems-2021\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TQY-NUMA2021.pdf\"},\"keyword\":[\"Bilevel variational inequality problem\",\"Hybrid steepest descent method\",\"Inertial extragradient method\",\"Projection and contraction method\",\"Pseudomonotone operator\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Liu\"],\"firstnames\":[\"Liya\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Qin\"],\"firstnames\":[\"Xiaolong\"],\"suffixes\":[]}],\"title\":\"Self adaptive inertial extragradient algorithms for solving bilevel pseudomonotone variational inequality problems\",\"journal\":\"Japan Journal of Industrial and Applied Mathematics\",\"year\":\"2021\",\"volume\":\"38\",\"number\":\"2\",\"pages\":\"519-543\",\"doi\":\"10.1007/s13160-020-00450-y\",\"url\":\"https://bingtan.me/files/paper/TLQ-JIAM2021.pdf\",\"abstract\":\"We introduce two inertial extragradient algorithms for solving a bilevel pseudomonotone variational inequality problem in real Hilbert spaces. The advantages of the proposed algorithms are that they can work without the prior knowledge of the Lipschitz constant of the involving operator and only one projection onto the feasible set is required. Strong convergence theorems of the suggested algorithms are obtained under suitable conditions. Finally, some numerical examples are provided to show the efficiency of the proposed algorithms.\",\"keywords\":\"Bilevel variational inequality problem, Inertial method, Subgradient extragradient method, Tseng's extragradient method, Pseudomonotone operator, Hybrid steepest descent method\",\"abbrev_source_title\":\"Jpn J. Ind. Appl. Math.\",\"bibbase_note\":\"<span style=\\\"color: red\\\">(<s>ESI Highly Cited Paper</s>)</span>\",\"bibtex\":\"@ARTICLE{TLQ_JIAM21,\\nauthor={Tan, Bing and Liu, Liya and Qin, Xiaolong},\\ntitle={Self adaptive inertial extragradient algorithms for solving bilevel pseudomonotone variational inequality problems},\\njournal={Japan Journal of Industrial and Applied Mathematics},\\nyear={2021},\\nvolume={38},\\nnumber={2},\\npages={519-543},\\ndoi={10.1007/s13160-020-00450-y},\\nurl={https://bingtan.me/files/paper/TLQ-JIAM2021.pdf},\\nabstract={We introduce two inertial extragradient algorithms for solving a bilevel pseudomonotone variational inequality problem in real Hilbert spaces. The advantages of the proposed algorithms are that they can work without the prior knowledge of the Lipschitz constant of the involving operator and only one projection onto the feasible set is required. Strong convergence theorems of the suggested algorithms are obtained under suitable conditions. Finally, some numerical examples are provided to show the efficiency of the proposed algorithms.},\\nkeywords={Bilevel variational inequality problem,  Inertial method, Subgradient extragradient method,  Tseng's extragradient method,  Pseudomonotone operator,  Hybrid steepest descent method},\\nabbrev_source_title={Jpn J. Ind. Appl. Math.},\\nbibbase_note={<span style=\\\"color: red\\\">(<s>ESI Highly Cited Paper</s>)</span>},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Liu, L.\",\"Qin, X.\"],\"key\":\"TLQ_JIAM21\",\"id\":\"TLQ_JIAM21\",\"bibbaseid\":\"tan-liu-qin-selfadaptiveinertialextragradientalgorithmsforsolvingbilevelpseudomonotonevariationalinequalityproblems-2021\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TLQ-JIAM2021.pdf\"},\"keyword\":[\"Bilevel variational inequality problem\",\"Inertial method\",\"Subgradient extragradient method\",\"Tseng's extragradient method\",\"Pseudomonotone operator\",\"Hybrid steepest descent method\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Fan\"],\"firstnames\":[\"Jingjing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Qin\"],\"firstnames\":[\"Xiaolong\"],\"suffixes\":[]}],\"title\":\"Inertial extragradient algorithms with non-monotonic step sizes for solving variational inequalities and fixed point problems\",\"journal\":\"Advances in Operator Theory\",\"year\":\"2021\",\"volume\":\"6\",\"number\":\"4\",\"doi\":\"10.1007/s43036-021-00155-0\",\"pages\":\"61\",\"url\":\"https://bingtan.me/files/paper/TFQ-AIOT2021.pdf\",\"abstract\":\"In this paper, we introduce four inertial extragradient algorithms with non-monotonic step sizes to find the solution of the convex feasibility problem, which consists of a monotone variational inequality problem and a fixed point problem with a demicontractive mapping. Strong convergence theorems of the suggested algorithms are established under some standard conditions. Finally, we implement some computational tests to show the efficiency and advantages of the proposed algorithms and compare them with some existing ones.\",\"keywords\":\"Fixed point problem, Inertial method, Strong convergence, Subgradient extragradient method, Tseng's extragradient method, Variational inequality problem\",\"abbrev_source_title\":\"Adv. Oper. Theory\",\"bibtex\":\"@ARTICLE{TFQ_AIOT21,\\nauthor={Tan, Bing and Fan, Jingjing and Qin, Xiaolong},\\ntitle={Inertial extragradient algorithms with non-monotonic step sizes for solving variational inequalities and fixed point problems},\\njournal={Advances in Operator Theory},\\nyear={2021},\\nvolume={6},\\nnumber={4},\\ndoi={10.1007/s43036-021-00155-0},\\npages={61},\\nurl={https://bingtan.me/files/paper/TFQ-AIOT2021.pdf},\\nabstract={In this paper, we introduce four inertial extragradient algorithms with non-monotonic step sizes to find the solution of the convex feasibility problem, which consists of a monotone variational inequality problem and a fixed point problem with a demicontractive mapping. Strong convergence theorems of the suggested algorithms are established under some standard conditions. Finally, we implement some computational tests to show the efficiency and advantages of the proposed algorithms and compare them with some existing ones.},\\nkeywords={Fixed point problem,  Inertial method,  Strong convergence,  Subgradient extragradient method,  Tseng's extragradient method,  Variational inequality problem},\\nabbrev_source_title={Adv. Oper. Theory},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Fan, J.\",\"Qin, X.\"],\"key\":\"TFQ_AIOT21\",\"id\":\"TFQ_AIOT21\",\"bibbaseid\":\"tan-fan-qin-inertialextragradientalgorithmswithnonmonotonicstepsizesforsolvingvariationalinequalitiesandfixedpointproblems-2021\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TFQ-AIOT2021.pdf\"},\"keyword\":[\"Fixed point problem\",\"Inertial method\",\"Strong convergence\",\"Subgradient extragradient method\",\"Tseng's extragradient method\",\"Variational inequality problem\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Li\"],\"firstnames\":[\"Songxiao\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Qin\"],\"firstnames\":[\"Xiaolong\"],\"suffixes\":[]}],\"title\":\"Self-adaptive inertial single projection methods for variational inequalities involving non-Lipschitz and Lipschitz operators with their applications to optimal control problems\",\"journal\":\"Applied Numerical Mathematics\",\"year\":\"2021\",\"volume\":\"170\",\"pages\":\"219–241\",\"doi\":\"10.1016/j.apnum.2021.07.022\",\"url\":\"https://bingtan.me/files/paper/TLQ-ANM2021.pdf\",\"abstract\":\"In this paper, four accelerated subgradient extragradient methods are proposed to solve the variational inequality problem with a pseudo-monotone operator in real Hilbert spaces. These iterative schemes employ two new adaptive stepsize strategies that are significant when the Lipschitz constant of the mapping involved is unknown. Strong convergence theorems for the proposed algorithms are established under the condition that the operators are Lipschitz continuous and non-Lipschitz continuous. Numerical experiments on finite- and infinite-dimensional spaces and applications in optimal control problems are reported to demonstrate the advantages and efficiency of the proposed algorithms over some existing results.\",\"keywords\":\"Inertial method, Subgradient extragradient method, Optimal control problem, Pseudomonotone operator, Non-Lipschitz operator, Variational inequality problem\",\"abbrev_source_title\":\"Appl Numer Math\",\"bibtex\":\"@ARTICLE{TLQ_ANM21,\\nauthor={Tan, Bing and Li, Songxiao and Qin, Xiaolong},\\ntitle={Self-adaptive inertial single projection methods for variational inequalities involving non-Lipschitz and Lipschitz operators with their applications to optimal control problems},\\njournal={Applied Numerical Mathematics},\\nyear={2021},\\nvolume={170},\\npages={219--241},\\ndoi={10.1016/j.apnum.2021.07.022},\\nurl={https://bingtan.me/files/paper/TLQ-ANM2021.pdf},\\nabstract={In this paper, four accelerated subgradient extragradient methods are proposed to solve the variational inequality problem with a pseudo-monotone operator in real Hilbert spaces. These iterative schemes employ two new adaptive stepsize strategies that are significant when the Lipschitz constant of the mapping involved is unknown. Strong convergence theorems for the proposed algorithms are established under the condition that the operators are Lipschitz continuous and non-Lipschitz continuous. Numerical experiments on finite- and infinite-dimensional spaces and applications in optimal control problems are reported to demonstrate the advantages and efficiency of the proposed algorithms over some existing results.},\\nkeywords={Inertial method, Subgradient extragradient method,  Optimal control problem,  Pseudomonotone operator,  Non-Lipschitz operator,  Variational inequality problem},\\nabbrev_source_title={Appl Numer Math},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Li, S.\",\"Qin, X.\"],\"key\":\"TLQ_ANM21\",\"id\":\"TLQ_ANM21\",\"bibbaseid\":\"tan-li-qin-selfadaptiveinertialsingleprojectionmethodsforvariationalinequalitiesinvolvingnonlipschitzandlipschitzoperatorswiththeirapplicationstooptimalcontrolproblems-2021\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TLQ-ANM2021.pdf\"},\"keyword\":[\"Inertial method\",\"Subgradient extragradient method\",\"Optimal control problem\",\"Pseudomonotone operator\",\"Non-Lipschitz operator\",\"Variational inequality problem\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Li\"],\"firstnames\":[\"Songxiao\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Qin\"],\"firstnames\":[\"Xiaolong\"],\"suffixes\":[]}],\"title\":\"An accelerated extragradient algorithm for bilevel pseudomonotone variational inequality problems with application to optimal control problems\",\"journal\":\"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas\",\"year\":\"2021\",\"volume\":\"115\",\"number\":\"4\",\"doi\":\"10.1007/s13398-021-01116-1\",\"pages\":\"174\",\"url\":\"https://bingtan.me/files/paper/TLQ-RACSAM2021.pdf\",\"abstract\":\"In this paper, an inertial extragradient algorithm with a new non-monotonic stepsize is proposed to solve the bilevel pseudomonotone variational inequality problem in real Hilbert spaces. The advantages of the suggested iterative algorithm are that only one projection onto the feasible set needs to be performed in each iteration and the prior knowledge of the Lipschitz constant of the mapping involved does not require to be known. The strong convergence theorem of the suggested algorithm is established under some suitable conditions. Numerical experiments are reported to illustrate the advantages and efficiency of the presented algorithm over the existing related ones.\",\"keywords\":\"Bilevel variational inequality problem, Hybrid steepest descent method, Inertial extragradient method, Projection and contraction method, Pseudomonotone operator\",\"abbrev_source_title\":\"Rev. R. Acad. Cienc. Exactas F ́is. Nat. Ser. A Mat. RACSAM\",\"bibtex\":\"@ARTICLE{TLQ_RCSM21,\\nauthor={Tan, Bing and Li, Songxiao and Qin, Xiaolong},\\ntitle={An accelerated extragradient algorithm for bilevel pseudomonotone variational inequality problems with application to optimal control problems},\\njournal={Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas},\\nyear={2021},\\nvolume={115},\\nnumber={4},\\ndoi={10.1007/s13398-021-01116-1},\\npages={174},\\nurl={https://bingtan.me/files/paper/TLQ-RACSAM2021.pdf},\\nabstract={In this paper, an inertial extragradient algorithm with a new non-monotonic stepsize is proposed to solve the bilevel pseudomonotone variational inequality problem in real Hilbert spaces. The advantages of the suggested iterative algorithm are that only one projection onto the feasible set needs to be performed in each iteration and the prior knowledge of the Lipschitz constant of the mapping involved does not require to be known. The strong convergence theorem of the suggested algorithm is established under some suitable conditions. Numerical experiments are reported to illustrate the advantages and efficiency of the presented algorithm over the existing related ones.},\\nkeywords={Bilevel variational inequality problem,  Hybrid steepest descent method,  Inertial extragradient method,  Projection and contraction method,  Pseudomonotone operator},\\nabbrev_source_title={Rev. R. Acad. Cienc. Exactas F{\\\\' i}s. Nat. Ser. A Mat. RACSAM},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Li, S.\",\"Qin, X.\"],\"key\":\"TLQ_RCSM21\",\"id\":\"TLQ_RCSM21\",\"bibbaseid\":\"tan-li-qin-anacceleratedextragradientalgorithmforbilevelpseudomonotonevariationalinequalityproblemswithapplicationtooptimalcontrolproblems-2021\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TLQ-RACSAM2021.pdf\"},\"keyword\":[\"Bilevel variational inequality problem\",\"Hybrid steepest descent method\",\"Inertial extragradient method\",\"Projection and contraction method\",\"Pseudomonotone operator\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Li\"],\"firstnames\":[\"Songxiao\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Qin\"],\"firstnames\":[\"Xiaolong\"],\"suffixes\":[]}],\"title\":\"On modified subgradient extragradient methods for pseudomonotone variational inequality problems with applications\",\"journal\":\"Computational and Applied Mathematics\",\"year\":\"2021\",\"volume\":\"40\",\"number\":\"7\",\"doi\":\"10.1007/s40314-021-01642-z\",\"pages\":\"253\",\"url\":\"https://bingtan.me/files/paper/TLQ-COAM2021.pdf\",\"abstract\":\"This paper presents several modified subgradient extragradient methods with inertial effects to approximate solutions of variational inequality problems in real Hilbert spaces. The operators involved are either pseudomonotone Lipschitz continuous or pseudomonotone non-Lipschitz continuous. The advantage of the suggested algorithms is that they can work adaptively without the prior information of the Lipschitz constant of the mapping involved. Strong convergence theorems of the proposed algorithms are established under some suitable conditions. Finally, some numerical experiments are given to verify the advantages and efficiency of the proposed iterative algorithms with respect to previously known ones.\",\"keywords\":\"Extragradient method, Non-Lipschitz operator, Optimal control problem, Pseudomonotone operator, Variational inequality problem\",\"abbrev_source_title\":\"Comput. Appl. Math.\",\"bibtex\":\"@ARTICLE{TLQ_COAM21,\\nauthor={Tan, Bing and Li, Songxiao and Qin, Xiaolong},\\ntitle={On modified subgradient extragradient methods for pseudomonotone variational inequality problems with applications},\\njournal={Computational and Applied Mathematics},\\nyear={2021},\\nvolume={40},\\nnumber={7},\\ndoi={10.1007/s40314-021-01642-z},\\npages={253},\\nurl={https://bingtan.me/files/paper/TLQ-COAM2021.pdf},\\nabstract={This paper presents several modified subgradient extragradient methods with inertial effects to approximate solutions of variational inequality problems in real Hilbert spaces. The operators involved are either pseudomonotone Lipschitz continuous or pseudomonotone non-Lipschitz continuous. The advantage of the suggested algorithms is that they can work adaptively without the prior information of the Lipschitz constant of the mapping involved. Strong convergence theorems of the proposed algorithms are established under some suitable conditions. Finally, some numerical experiments are given to verify the advantages and efficiency of the proposed iterative algorithms with respect to previously known ones.},\\nkeywords={Extragradient method,  Non-Lipschitz operator,  Optimal control problem,  Pseudomonotone operator,  Variational inequality problem},\\nabbrev_source_title={Comput. Appl. Math.},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Li, S.\",\"Qin, X.\"],\"key\":\"TLQ_COAM21\",\"id\":\"TLQ_COAM21\",\"bibbaseid\":\"tan-li-qin-onmodifiedsubgradientextragradientmethodsforpseudomonotonevariationalinequalityproblemswithapplications-2021\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TLQ-COAM2021.pdf\"},\"keyword\":[\"Extragradient method\",\"Non-Lipschitz operator\",\"Optimal control problem\",\"Pseudomonotone operator\",\"Variational inequality problem\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Fan\"],\"firstnames\":[\"Jingjing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Li\"],\"firstnames\":[\"Songxiao\"],\"suffixes\":[]}],\"title\":\"Self-adaptive inertial extragradient algorithms for solving variational inequality problems\",\"journal\":\"Computational and Applied Mathematics\",\"year\":\"2021\",\"volume\":\"40\",\"number\":\"1\",\"doi\":\"10.1007/s40314-020-01393-3\",\"pages\":\"19\",\"url\":\"https://bingtan.me/files/paper/TFL-COAM2021.pdf\",\"abstract\":\"In this paper, we study the strong convergence of two Mann-type inertial extragradient algorithms, which are devised with a new step size, for solving a variational inequality problem with a monotone and Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems for the suggested algorithms are proved without the prior knowledge of the Lipschitz constant of the operator. Finally, we provide some numerical experiments to illustrate the performance of the proposed algorithms and provide a comparison with related ones.\",\"keywords\":\"Inertial method, Mann method, Subgradient extragradient method, Tseng's extragradient method, Variational inequality problem\",\"abbrev_source_title\":\"Comput. Appl. Math.\",\"bibbase_note\":\"<span style=\\\"color: red\\\">(<s>ESI Highly Cited Paper</s>)</span>\",\"bibtex\":\"@ARTICLE{TFL_COAM21,\\nauthor={Tan, Bing and Fan, Jingjing and Li, Songxiao},\\ntitle={Self-adaptive inertial extragradient algorithms for solving variational inequality problems},\\njournal={Computational and Applied Mathematics},\\nyear={2021},\\nvolume={40},\\nnumber={1},\\ndoi={10.1007/s40314-020-01393-3},\\npages={19},\\nurl={https://bingtan.me/files/paper/TFL-COAM2021.pdf},\\nabstract={In this paper, we study the strong convergence of two Mann-type inertial extragradient algorithms, which are devised with a new step size, for solving a variational inequality problem with a monotone and Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems for the suggested algorithms are proved without the prior knowledge of the Lipschitz constant of the operator. Finally, we provide some numerical experiments to illustrate the performance of the proposed algorithms and provide a comparison with related ones.},\\nkeywords={Inertial method,  Mann method,  Subgradient extragradient method,  Tseng's extragradient method,  Variational inequality problem},\\nabbrev_source_title={Comput. Appl. Math.},\\nbibbase_note={<span style=\\\"color: red\\\">(<s>ESI Highly Cited Paper</s>)</span>},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Fan, J.\",\"Li, S.\"],\"key\":\"TFL_COAM21\",\"id\":\"TFL_COAM21\",\"bibbaseid\":\"tan-fan-li-selfadaptiveinertialextragradientalgorithmsforsolvingvariationalinequalityproblems-2021\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TFL-COAM2021.pdf\"},\"keyword\":[\"Inertial method\",\"Mann method\",\"Subgradient extragradient method\",\"Tseng's extragradient method\",\"Variational inequality problem\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Cho\"],\"firstnames\":[\"Sun\",\"Y.\"],\"suffixes\":[]}],\"title\":\"Self-adaptive inertial shrinking projection algorithms for solving pseudomonotone variational inequalities\",\"journal\":\"Journal of Nonlinear and Convex Analysis\",\"year\":\"2021\",\"volume\":\"22\",\"number\":\"3\",\"pages\":\"613–627\",\"url\":\"https://bingtan.me/files/paper/TC-JNCA2021.pdf\",\"abstract\":\"In this paper, we construct two fast iterative methods to solve pseudomonotone variational inequalities in real Hilbert spaces. The advantage of the suggested iterative schemes is that they can adaptively update the iterative step size through some previously known information without performing any line search process. Strong convergence theorems of the proposed algorithms are established under some relaxed conditions imposed on the parameters. Finally, several numerical tests are given to show the advantages and efficiency of the proposed approaches compared with the existing results.\",\"keywords\":\"Inertial method, Subgradient extragradient method, Tseng's extragradient method, Pseudomonotone operator, Shrinking projection method, Variational inequality problem\",\"abbrev_source_title\":\"J. Nonlinear Convex Anal.\",\"bibtex\":\"@ARTICLE{TC_JNCA21,\\nauthor={Tan, Bing and Cho, Sun Y.},\\ntitle={Self-adaptive inertial shrinking projection algorithms for solving pseudomonotone variational inequalities},\\njournal={Journal of Nonlinear and Convex Analysis},\\nyear={2021},\\nvolume={22},\\nnumber={3},\\npages={613--627},\\nurl={https://bingtan.me/files/paper/TC-JNCA2021.pdf},\\nabstract={In this paper, we construct two fast iterative methods to solve pseudomonotone variational inequalities in real Hilbert spaces. The advantage of the suggested iterative schemes is that they can adaptively update the iterative step size through some previously known information without performing any line search process. Strong convergence theorems of the proposed algorithms are established under some relaxed conditions imposed on the parameters. Finally, several numerical tests are given to show the advantages and efficiency of the proposed approaches compared with the existing results.},\\nkeywords={Inertial method, Subgradient extragradient method,  Tseng's extragradient method,  Pseudomonotone operator,  Shrinking projection method,  Variational inequality problem},\\nabbrev_source_title={J. Nonlinear Convex Anal.},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Cho, S. Y.\"],\"key\":\"TC_JNCA21\",\"id\":\"TC_JNCA21\",\"bibbaseid\":\"tan-cho-selfadaptiveinertialshrinkingprojectionalgorithmsforsolvingpseudomonotonevariationalinequalities-2021\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TC-JNCA2021.pdf\"},\"keyword\":[\"Inertial method\",\"Subgradient extragradient method\",\"Tseng's extragradient method\",\"Pseudomonotone operator\",\"Shrinking projection method\",\"Variational inequality problem\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Cho\"],\"firstnames\":[\"Sun\",\"Y.\"],\"suffixes\":[]}],\"title\":\"Inertial extragradient methods for solving pseudomonotone variational inequalities with non-lipschitz mappings and their optimization applications\",\"journal\":\"Applied Set-Valued Analysis and Optimization\",\"year\":\"2021\",\"volume\":\"3\",\"number\":\"2\",\"pages\":\"165–192\",\"doi\":\"10.23952/asvao.3.2021.2.03\",\"url\":\"https://bingtan.me/files/paper/TC-ASVAO2021.pdf\",\"abstract\":\"In this paper, four extragradient-type algorithms with inertial terms are presented for solving the variational inequality problem with a pseudomonotone and non-Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems of the suggested methods are established under some suitable conditions imposed on the parameters. Finally, several computational tests and applications in optimal control problems are given to illustrate the efficiency and advantages of the proposed iterative schemes over some known ones.\",\"keywords\":\"Inertial extragradient method, Non-Lipschitz operator, Pseudomonotone operator, Variational inequality problem, Viscosity method\",\"abbrev_source_title\":\"Appl. Set-Valued. Anal. Optim.\",\"bibtex\":\"@ARTICLE{TC_ASVAO21,\\nauthor={Tan, Bing and Cho, Sun Y.},\\ntitle={Inertial extragradient methods for solving pseudomonotone variational inequalities with non-lipschitz mappings and their optimization applications},\\njournal={Applied Set-Valued Analysis and Optimization},\\nyear={2021},\\nvolume={3},\\nnumber={2},\\npages={165--192},\\ndoi={10.23952/asvao.3.2021.2.03},\\nurl={https://bingtan.me/files/paper/TC-ASVAO2021.pdf},\\nabstract={In this paper, four extragradient-type algorithms with inertial terms are presented for solving the variational inequality problem with a pseudomonotone and non-Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems of the suggested methods are established under some suitable conditions imposed on the parameters. Finally, several computational tests and applications in optimal control problems are given to illustrate the efficiency and advantages of the proposed iterative schemes over some known ones.},\\nkeywords={Inertial extragradient method,  Non-Lipschitz operator,  Pseudomonotone operator,  Variational inequality problem,  Viscosity method},\\nabbrev_source_title={Appl. Set-Valued. Anal. Optim.},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Cho, S. Y.\"],\"key\":\"TC_ASVAO21\",\"id\":\"TC_ASVAO21\",\"bibbaseid\":\"tan-cho-inertialextragradientmethodsforsolvingpseudomonotonevariationalinequalitieswithnonlipschitzmappingsandtheiroptimizationapplications-2021\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TC-ASVAO2021.pdf\"},\"keyword\":[\"Inertial extragradient method\",\"Non-Lipschitz operator\",\"Pseudomonotone operator\",\"Variational inequality problem\",\"Viscosity method\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Liu\"],\"firstnames\":[\"Liya\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Latif\"],\"firstnames\":[\"A.\"],\"suffixes\":[]}],\"title\":\"Approximation of fixed points for a semigroup of Bregman quasi-nonexpansive mappings in Banach spaces\",\"journal\":\"Journal of Nonlinear and Variational Analysis\",\"year\":\"2021\",\"volume\":\"5\",\"number\":\"1\",\"pages\":\"9–22\",\"doi\":\"10.23952/jnva.5.2021.1.02\",\"url\":\"https://bingtan.me/files/paper/LTL-JNVA2021.pdf\",\"abstract\":\"The purpose of this paper is to study the iterative scheme of the Halpern type for a commutative semigroup $\\\\mathfrak{J}=łeft\\\\{S_{λ}: λ ∈ \\\\mathcal{Q}i̊ght\\\\}$ of Bregman quasi-nonexpansive mappings on a closed and convex subset of a Banach space. A strong convergence theorem is established for finding a common fixed point solution. Our results extend and improve some related results in the current literature. In addition, we present numerical examples to illustrate the performance of our method in finite and infinite dimensional spaces.\",\"keywords\":\"Banach space, Bregman quasi-nonexpansive, Fixed point problem, Halpern method, Strong convergence\",\"abbrev_source_title\":\"J. Nonlinear Var. Anal.\",\"bibtex\":\"@ARTICLE{LTL_JNVA21,\\nauthor={Liu, Liya and Tan, Bing and Latif, A.},\\ntitle={Approximation of fixed points for a semigroup of Bregman quasi-nonexpansive mappings in {B}anach spaces},\\njournal={Journal of Nonlinear and Variational Analysis},\\nyear={2021},\\nvolume={5},\\nnumber={1},\\npages={9--22},\\ndoi={10.23952/jnva.5.2021.1.02},\\nurl={https://bingtan.me/files/paper/LTL-JNVA2021.pdf},\\nabstract={The purpose of this paper is to study the iterative scheme of the Halpern type for a commutative semigroup $\\\\mathfrak{J}=\\\\left\\\\{S_{\\\\lambda}: \\\\lambda \\\\in \\\\mathcal{Q}\\\\right\\\\}$ of Bregman quasi-nonexpansive mappings on a closed and convex subset of a Banach space. A strong convergence theorem is established for finding a common fixed point solution. Our results extend and improve some related results in the current literature. In addition, we present numerical examples to illustrate the performance of our method in finite and infinite dimensional spaces.},\\nkeywords={Banach space,  Bregman quasi-nonexpansive,  Fixed point problem,  Halpern method,  Strong convergence},\\nabbrev_source_title={J. Nonlinear Var. Anal.},\\n}\\n\\n\",\"author_short\":[\"Liu, L.\",\"Tan, B.\",\"Latif, A.\"],\"key\":\"LTL_JNVA21\",\"id\":\"LTL_JNVA21\",\"bibbaseid\":\"liu-tan-latif-approximationoffixedpointsforasemigroupofbregmanquasinonexpansivemappingsinbanachspaces-2021\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/LTL-JNVA2021.pdf\"},\"keyword\":[\"Banach space\",\"Bregman quasi-nonexpansive\",\"Fixed point problem\",\"Halpern method\",\"Strong convergence\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Zhou\"],\"firstnames\":[\"Zheng\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Li\"],\"firstnames\":[\"Songxiao\"],\"suffixes\":[]}],\"title\":\"An accelerated hybrid projection method with a self-adaptive step-size sequence for solving split common fixed point problems\",\"journal\":\"Mathematical Methods in the Applied Sciences\",\"year\":\"2021\",\"volume\":\"44\",\"number\":\"8\",\"pages\":\"7294–7303\",\"doi\":\"10.1002/mma.7261\",\"url\":\"https://bingtan.me/files/paper/ZTL-MMAS2021.pdf\",\"abstract\":\"This paper attempts to solve the split common fixed point problem for demicontractive mappings. We give an accelerated hybrid projection algorithm that combines the hybrid projection method and the inertial technique. The strong convergence theorem of this algorithm is obtained under mild conditions by a self-adaptive step-size sequence, which does not need prior knowledge of the operator norm. Some numerical experiments in infinite-dimensional Hilbert spaces are provided to illustrate the reliability and robustness of the algorithm and also to compare it with existing ones.\",\"keywords\":\"Demicontractive mapping, Hybrid projection method, Inertial method, Split common fixed point problem\",\"abbrev_source_title\":\"Math. Methods Appl. Sci.\",\"bibbase_note\":\"<span style=\\\"color: red\\\">(<s>ESI Highly Cited Paper</s>)</span>\",\"bibtex\":\"@ARTICLE{ZTL_MMAS21,\\nauthor={Zhou, Zheng and Tan, Bing and Li, Songxiao},\\ntitle={An accelerated hybrid projection method with a self-adaptive step-size sequence for solving split common fixed point problems},\\njournal={Mathematical Methods in the Applied Sciences},\\nyear={2021},\\nvolume={44},\\nnumber={8},\\npages={7294--7303},\\ndoi={10.1002/mma.7261},\\nurl={https://bingtan.me/files/paper/ZTL-MMAS2021.pdf},\\nabstract={This paper attempts to solve the split common fixed point problem for demicontractive mappings. We give an accelerated hybrid projection algorithm that combines the hybrid projection method and the inertial technique. The strong convergence theorem of this algorithm is obtained under mild conditions by a self-adaptive step-size sequence, which does not need prior knowledge of the operator norm. Some numerical experiments in infinite-dimensional Hilbert spaces are provided to illustrate the reliability and robustness of the algorithm and also to compare it with existing ones.},\\nkeywords={Demicontractive mapping,  Hybrid projection method,  Inertial method,  Split common fixed point problem},\\nabbrev_source_title={Math. Methods Appl. Sci.},\\nbibbase_note={<span style=\\\"color: red\\\">(<s>ESI Highly Cited Paper</s>)</span>},\\n}\\n\\n\",\"author_short\":[\"Zhou, Z.\",\"Tan, B.\",\"Li, S.\"],\"key\":\"ZTL_MMAS21\",\"id\":\"ZTL_MMAS21\",\"bibbaseid\":\"zhou-tan-li-anacceleratedhybridprojectionmethodwithaselfadaptivestepsizesequenceforsolvingsplitcommonfixedpointproblems-2021\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/ZTL-MMAS2021.pdf\"},\"keyword\":[\"Demicontractive mapping\",\"Hybrid projection method\",\"Inertial method\",\"Split common fixed point problem\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Fan\"],\"firstnames\":[\"Jingjing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Li\"],\"firstnames\":[\"Songxiao\"],\"suffixes\":[]}],\"title\":\"An explicit extragradient algorithm for equilibrium problems on HHadamard manifolds\",\"journal\":\"Computational and Applied Mathematics\",\"year\":\"2021\",\"volume\":\"40\",\"number\":\"2\",\"doi\":\"10.1007/s40314-021-01427-4\",\"pages\":\"68\",\"url\":\"https://bingtan.me/files/paper/FTL-COAM2021.pdf\",\"abstract\":\"In this paper, we investigate a new extragradient algorithm for solving pseudomonotone equilibrium problems on Hadamard manifolds. Our algorithm uses a variable stepsize, which is updated at each iteration and based on some previous iterates. The convergence analysis of the proposed algorithm is discussed under mild assumptions. In the case where the equilibrium bifunction is strongly pseudomonotone, the R-linear rate of convergence of the new algorithm is formulated. A fundamental experiment is provided to illustrate the numerical behavior of the algorithm.\",\"keywords\":\"Equilibrium problem, Extragradient method, Hadamard manifolds, Lipschitz-type bifunction, Pseudomonotone bifunction\",\"abbrev_source_title\":\"Comput. Appl. Math.\",\"bibtex\":\"@ARTICLE{FTL_COAM21,\\nauthor={Fan, Jingjing and Tan, Bing and Li, Songxiao},\\ntitle={An explicit extragradient algorithm for equilibrium problems on {H}{H}adamard manifolds},\\njournal={Computational and Applied Mathematics},\\nyear={2021},\\nvolume={40},\\nnumber={2},\\ndoi={10.1007/s40314-021-01427-4},\\npages={68},\\nurl={https://bingtan.me/files/paper/FTL-COAM2021.pdf},\\nabstract={In this paper, we investigate a new extragradient algorithm for solving pseudomonotone equilibrium problems on Hadamard manifolds. Our algorithm uses a variable stepsize, which is updated at each iteration and based on some previous iterates. The convergence analysis of the proposed algorithm is discussed under mild assumptions. In the case where the equilibrium bifunction is strongly pseudomonotone, the R-linear rate of convergence of the new algorithm is formulated. A fundamental experiment is provided to illustrate the numerical behavior of the algorithm.},\\nkeywords={Equilibrium problem,  Extragradient method,  Hadamard manifolds,  Lipschitz-type bifunction,  Pseudomonotone bifunction},\\nabbrev_source_title={Comput. Appl. Math.},\\n}\\n\\n\",\"author_short\":[\"Fan, J.\",\"Tan, B.\",\"Li, S.\"],\"key\":\"FTL_COAM21\",\"id\":\"FTL_COAM21\",\"bibbaseid\":\"fan-tan-li-anexplicitextragradientalgorithmforequilibriumproblemsonhhadamardmanifolds-2021\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/FTL-COAM2021.pdf\"},\"keyword\":[\"Equilibrium problem\",\"Extragradient method\",\"Hadamard manifolds\",\"Lipschitz-type bifunction\",\"Pseudomonotone bifunction\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Fan\"],\"firstnames\":[\"Jingjing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Qin\"],\"firstnames\":[\"Xiaolong\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]}],\"title\":\"Convergence of an inertial shadow Douglas-Rachford splitting algorithm for monotone inclusions\",\"journal\":\"Numerical Functional Analysis and Optimization\",\"year\":\"2021\",\"volume\":\"42\",\"number\":\"14\",\"pages\":\"1627–1644\",\"doi\":\"10.1080/01630563.2021.2001749\",\"url\":\"https://bingtan.me/files/paper/FQT-NFAO2021.pdf\",\"abstract\":\"An inertial shadow Douglas-Rachford splitting algorithm for finding zeros of the sum of monotone operators is proposed in Hilbert spaces. Moreover, a three-operator splitting algorithm for solving a class of monotone inclusion problems is also concerned. The weak convergence of the algorithms is investigated under mild assumptions. Some numerical experiments are implemented to illustrate our main convergence results.\",\"keywords\":\"Inertial method, Monotone inclusion, Shadow Douglas-Rachford splitting algorithm, Three-operator splitting\",\"abbrev_source_title\":\"Numer. Funct. Anal. Optim.\",\"bibtex\":\"@ARTICLE{FQT_NFAO21,\\nauthor={Fan, Jingjing and Qin, Xiaolong and Tan, Bing},\\ntitle={Convergence of an inertial shadow {D}ouglas-{R}achford splitting algorithm for monotone inclusions},\\njournal={Numerical Functional Analysis and Optimization},\\nyear={2021},\\nvolume={42},\\nnumber={14},\\npages={1627--1644},\\ndoi={10.1080/01630563.2021.2001749},\\nurl={https://bingtan.me/files/paper/FQT-NFAO2021.pdf},\\nabstract={An inertial shadow Douglas-Rachford splitting algorithm for finding zeros of the sum of monotone operators is proposed in Hilbert spaces. Moreover, a three-operator splitting algorithm for solving a class of monotone inclusion problems is also concerned. The weak convergence of the algorithms is investigated under mild assumptions. Some numerical experiments are implemented to illustrate our main convergence results.},\\nkeywords={Inertial method,  Monotone inclusion,  Shadow Douglas-Rachford splitting algorithm,  Three-operator splitting},\\nabbrev_source_title={Numer. Funct. Anal. Optim.},\\n}\\n\\n\",\"author_short\":[\"Fan, J.\",\"Qin, X.\",\"Tan, B.\"],\"key\":\"FQT_NFAO21\",\"id\":\"FQT_NFAO21\",\"bibbaseid\":\"fan-qin-tan-convergenceofaninertialshadowdouglasrachfordsplittingalgorithmformonotoneinclusions-2021\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/FQT-NFAO2021.pdf\"},\"keyword\":[\"Inertial method\",\"Monotone inclusion\",\"Shadow Douglas-Rachford splitting algorithm\",\"Three-operator splitting\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Li\"],\"firstnames\":[\"Songxiao\"],\"suffixes\":[]}],\"title\":\"Strong convergence of inertial mann algorithms for solving hierarchical fixed point problems\",\"journal\":\"Journal of Nonlinear and Variational Analysis\",\"year\":\"2020\",\"volume\":\"4\",\"number\":\"3\",\"pages\":\"337–355\",\"doi\":\"10.23952/jnva.4.2020.3.02\",\"url\":\"https://bingtan.me/files/paper/TL-JNVA2020.pdf\",\"abstract\":\"The paper introduces two inertial Mann algorithms to find solutions of hierarchical fixed point problems of nonexpansive mappings. We obtain strong convergence theorems in Hilbert spaces under suitable conditions. Some numerical examples are provided to illustrate the numerical behavior of the algorithms and numerical results show that our proposed algorithms are efficient and robust.\",\"keywords\":\"Hierarchical fixed point problem, Inertial method, Mann method, Nonexpansive mapping, Strong convergence, Viscosity method\",\"abbrev_source_title\":\"J. Nonlinear Var. Anal.\",\"bibtex\":\"@ARTICLE{TL_JNVA20,\\nauthor={Tan, Bing and Li, Songxiao},\\ntitle={Strong convergence of inertial mann algorithms for solving hierarchical fixed point problems},\\njournal={Journal of Nonlinear and Variational Analysis},\\nyear={2020},\\nvolume={4},\\nnumber={3},\\npages={337--355},\\ndoi={10.23952/jnva.4.2020.3.02},\\nurl={https://bingtan.me/files/paper/TL-JNVA2020.pdf},\\nabstract={The paper introduces two inertial Mann algorithms to find solutions of hierarchical fixed point problems of nonexpansive mappings. We obtain strong convergence theorems in Hilbert spaces under suitable conditions. Some numerical examples are provided to illustrate the numerical behavior of the algorithms and numerical results show that our proposed algorithms are efficient and robust.},\\nkeywords={Hierarchical fixed point problem,  Inertial method, Mann method,  Nonexpansive mapping,  Strong convergence,  Viscosity method},\\nabbrev_source_title={J. Nonlinear Var. Anal.},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Li, S.\"],\"key\":\"TL_JNVA20\",\"id\":\"TL_JNVA20\",\"bibbaseid\":\"tan-li-strongconvergenceofinertialmannalgorithmsforsolvinghierarchicalfixedpointproblems-2020\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TL-JNVA2020.pdf\"},\"keyword\":[\"Hierarchical fixed point problem\",\"Inertial method\",\"Mann method\",\"Nonexpansive mapping\",\"Strong convergence\",\"Viscosity method\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Cho\"],\"firstnames\":[\"Sun\",\"Y.\"],\"suffixes\":[]}],\"title\":\"An inertial mann-like algorithm for fixed points of nonexpansive mappings in Hilbert spaces\",\"journal\":\"Journal of Applied and Numerical Optimization\",\"year\":\"2020\",\"volume\":\"2\",\"number\":\"3\",\"pages\":\"335–351\",\"doi\":\"10.23952/jano.2.2020.3.05\",\"url\":\"https://bingtan.me/files/paper/TC-JANO2020.pdf\",\"abstract\":\"In this paper, we investigate an inertial Mann-like algorithm for fixed points of nonexpansive mappings in Hilbert spaces and obtain strong convergence results under some mild assumptions. Based on this, we derive a forward-backward algorithm involving Tikhonov regularization terms, which converges strongly to the solution of the monotone inclusion problem. We demonstrate the advantages of our algorithms comparing with some existing ones in the literature via split feasibility problem, variational inequality problem and signal recovery problem.\",\"keywords\":\"Forward-backward splitting algorithm, Inertial method, Mann method, Nonexpansive mapping, Strong convergence, Tikhonov regularization\",\"abbrev_source_title\":\"J. Appl. Numer. Optim.\",\"bibtex\":\"@ARTICLE{TC_JANO20,\\nauthor={Tan, Bing and Cho, Sun Y.},\\ntitle={An inertial mann-like algorithm for fixed points of nonexpansive mappings in {H}ilbert spaces},\\njournal={Journal of Applied and Numerical Optimization},\\nyear={2020},\\nvolume={2},\\nnumber={3},\\npages={335--351},\\ndoi={10.23952/jano.2.2020.3.05},\\nurl={https://bingtan.me/files/paper/TC-JANO2020.pdf},\\nabstract={In this paper, we investigate an inertial Mann-like algorithm for fixed points of nonexpansive mappings in Hilbert spaces and obtain strong convergence results under some mild assumptions. Based on this, we derive a forward-backward algorithm involving Tikhonov regularization terms, which converges strongly to the solution of the monotone inclusion problem. We demonstrate the advantages of our algorithms comparing with some existing ones in the literature via split feasibility problem, variational inequality problem and signal recovery problem.},\\nkeywords={Forward-backward splitting algorithm,  Inertial method, Mann method,  Nonexpansive mapping,  Strong convergence,  Tikhonov regularization},\\nabbrev_source_title={J. Appl. Numer. Optim.},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Cho, S. Y.\"],\"key\":\"TC_JANO20\",\"id\":\"TC_JANO20\",\"bibbaseid\":\"tan-cho-aninertialmannlikealgorithmforfixedpointsofnonexpansivemappingsinhilbertspaces-2020\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TC-JANO2020.pdf\"},\"keyword\":[\"Forward-backward splitting algorithm\",\"Inertial method\",\"Mann method\",\"Nonexpansive mapping\",\"Strong convergence\",\"Tikhonov regularization\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"downloads\":1,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Xu\"],\"firstnames\":[\"Shanshan\"],\"suffixes\":[]}],\"title\":\"Strong convergence of two inertial projection algorithms in Hilbert spaces\",\"journal\":\"Journal of Applied and Numerical Optimization\",\"year\":\"2020\",\"volume\":\"2\",\"number\":\"2\",\"pages\":\"171–186\",\"doi\":\"10.23952/jano.2.2020.2.04\",\"url\":\"https://bingtan.me/files/paper/TX-JANO2020.pdf\",\"abstract\":\"In this paper, we propose two inertial projection algorithms for finding a common solution of monotone variational inclusions and hierarchical fixed point problems of nonexpansive mappings. We obtain two strong convergence theorems under some suitable conditions in Hilbert spaces. In addition, we also give numerical examples to compare our algorithms with the existing ones. Numerical results show that our proposed algorithms are efficient and robust.\",\"keywords\":\"Hierarchical fixed point problem, Inertial method, Monotone operator, Strong convergence, Inclusion problem\",\"abbrev_source_title\":\"J. Appl. Numer. Optim.\",\"bibtex\":\"@ARTICLE{TX_JANO20,\\nauthor={Tan, Bing and Xu, Shanshan},\\ntitle={Strong convergence of two inertial projection algorithms in {H}ilbert spaces},\\njournal={Journal of Applied and Numerical Optimization},\\nyear={2020},\\nvolume={2},\\nnumber={2},\\npages={171--186},\\ndoi={10.23952/jano.2.2020.2.04},\\nurl={https://bingtan.me/files/paper/TX-JANO2020.pdf},\\nabstract={In this paper, we propose two inertial projection algorithms for finding a common solution of monotone variational inclusions and hierarchical fixed point problems of nonexpansive mappings. We obtain two strong convergence theorems under some suitable conditions in Hilbert spaces. In addition, we also give numerical examples to compare our algorithms with the existing ones. Numerical results show that our proposed algorithms are efficient and robust.},\\nkeywords={Hierarchical fixed point problem,  Inertial method,  Monotone operator,  Strong convergence,  Inclusion problem},\\nabbrev_source_title={J. Appl. Numer. Optim.},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Xu, S.\"],\"key\":\"TX_JANO20\",\"id\":\"TX_JANO20\",\"bibbaseid\":\"tan-xu-strongconvergenceoftwoinertialprojectionalgorithmsinhilbertspaces-2020\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TX-JANO2020.pdf\"},\"keyword\":[\"Hierarchical fixed point problem\",\"Inertial method\",\"Monotone operator\",\"Strong convergence\",\"Inclusion problem\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Zhou\"],\"firstnames\":[\"Zheng\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Qin\"],\"firstnames\":[\"Xiaolong\"],\"suffixes\":[]}],\"title\":\"Accelerated projection-based forward-backward splitting algorithms for monotone inclusion problems\",\"journal\":\"Journal of Applied Analysis and Computation\",\"year\":\"2020\",\"volume\":\"10\",\"number\":\"5\",\"pages\":\"2184–2197\",\"doi\":\"10.11948/20190363\",\"url\":\"https://bingtan.me/files/paper/TZQ-JAAC2020.pdf\",\"abstract\":\"In this paper, based on inertial and Tseng's ideas, we propose two projection-based algorithms to solve a monotone inclusion problem in infinite dimensional Hilbert spaces. Solution theorems of strong convergence are obtained under the certain conditions. Some numerical experiments are presented to illustrate that our algorithms are efficient than the existing results.\",\"keywords\":\"Forward-backward splitting algorithm, Inclusion problem, Monotone operator, Strong convergence\",\"abbrev_source_title\":\"J. Appl. Anal. Comput.\",\"bibtex\":\"@ARTICLE{TZQ_JAAC20,\\nauthor={Tan, Bing and Zhou, Zheng and Qin, Xiaolong},\\ntitle={Accelerated projection-based forward-backward splitting algorithms for monotone inclusion problems},\\njournal={Journal of Applied Analysis and Computation},\\nyear={2020},\\nvolume={10},\\nnumber={5},\\npages={2184--2197},\\ndoi={10.11948/20190363},\\nurl={https://bingtan.me/files/paper/TZQ-JAAC2020.pdf},\\nabstract={In this paper, based on inertial and Tseng's ideas, we propose two projection-based algorithms to solve a monotone inclusion problem in infinite dimensional Hilbert spaces. Solution theorems of strong convergence are obtained under the certain conditions. Some numerical experiments are presented to illustrate that our algorithms are efficient than the existing results.},\\nkeywords={Forward-backward splitting algorithm,  Inclusion problem,  Monotone operator,  Strong convergence},\\nabbrev_source_title={J. Appl. Anal. Comput.},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Zhou, Z.\",\"Qin, X.\"],\"key\":\"TZQ_JAAC20\",\"id\":\"TZQ_JAAC20\",\"bibbaseid\":\"tan-zhou-qin-acceleratedprojectionbasedforwardbackwardsplittingalgorithmsformonotoneinclusionproblems-2020\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TZQ-JAAC2020.pdf\"},\"keyword\":[\"Forward-backward splitting algorithm\",\"Inclusion problem\",\"Monotone operator\",\"Strong convergence\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Xu\"],\"firstnames\":[\"Shanshan\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Li\"],\"firstnames\":[\"Songxiao\"],\"suffixes\":[]}],\"title\":\"Inertial shrinking projection algorithms for solving hierarchical variational inequality problems\",\"journal\":\"Journal of Nonlinear and Convex Analysis\",\"year\":\"2020\",\"volume\":\"21\",\"number\":\"4\",\"pages\":\"871–884\",\"url\":\"https://bingtan.me/files/paper/TXL-JNCA2020.pdf\",\"abstract\":\"In this paper, we propose two inertial shrinking algorithms to approximate a solution of hierarchical variational inequality problems with nonex-pansive mappings in Hilbert spaces. We prove strong convergence theorems under some mild conditions. Finally, we present some numerical examples to compare our algorithms with some existing algorithms, which illustrate the advantage of our proposed algorithms.\",\"keywords\":\"Hierarchical variational inequality problem, Inertial method, Mann method, Nonexpansive mapping, Shrinking projection method, Strong convergence\",\"abbrev_source_title\":\"J. Nonlinear Convex Anal.\",\"bibbase_note\":\"<span style=\\\"color: red\\\">(<s>ESI Highly Cited Paper</s>)</span>\",\"bibtex\":\"@ARTICLE{TXL_JNCA20_2,\\nauthor={Tan, Bing and Xu, Shanshan and Li, Songxiao},\\ntitle={Inertial shrinking projection algorithms for solving hierarchical variational inequality problems},\\njournal={Journal of Nonlinear and Convex Analysis},\\nyear={2020},\\nvolume={21},\\nnumber={4},\\npages={871--884},\\nurl={https://bingtan.me/files/paper/TXL-JNCA2020.pdf},\\nabstract={In this paper, we propose two inertial shrinking algorithms to approximate a solution of hierarchical variational inequality problems with nonex-pansive mappings in Hilbert spaces. We prove strong convergence theorems under some mild conditions. Finally, we present some numerical examples to compare our algorithms with some existing algorithms, which illustrate the advantage of our proposed algorithms.},\\nkeywords={Hierarchical variational inequality problem,  Inertial method, Mann method,  Nonexpansive mapping,  Shrinking projection method,  Strong convergence},\\nabbrev_source_title={J. Nonlinear Convex Anal.},\\nbibbase_note={<span style=\\\"color: red\\\">(<s>ESI Highly Cited Paper</s>)</span>},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Xu, S.\",\"Li, S.\"],\"key\":\"TXL_JNCA20_2\",\"id\":\"TXL_JNCA20_2\",\"bibbaseid\":\"tan-xu-li-inertialshrinkingprojectionalgorithmsforsolvinghierarchicalvariationalinequalityproblems-2020\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TXL-JNCA2020.pdf\"},\"keyword\":[\"Hierarchical variational inequality problem\",\"Inertial method\",\"Mann method\",\"Nonexpansive mapping\",\"Shrinking projection method\",\"Strong convergence\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Xu\"],\"firstnames\":[\"Shanshan\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Li\"],\"firstnames\":[\"Songxiao\"],\"suffixes\":[]}],\"title\":\"Inertial hybrid and shrinking projection algorithms for solving variational inequality problems\",\"journal\":\"Journal of Nonlinear and Convex Analysis\",\"year\":\"2020\",\"volume\":\"21\",\"number\":\"10\",\"pages\":\"2193–2206\",\"url\":\"https://bingtan.me/files/paper/TXL-JNCA2020-10.pdf\",\"abstract\":\"In this paper, we propose two inertial hybrid and shrinking projection algorithms for strict pseudo-contractions in Hilbert spaces and obtain strong theorems in general conditions. In addition, we also propose two new inertial hybrid and shrinking projection algorithms without extrapolating step for non-expansive mappings in Hilbert spaces and get strong convergence results. Finally, we give some numerical examples to illustrate the computational performance of our proposed algorithms.\",\"keywords\":\"Variational inequality problem, Inertial method, Hybrid projection method, Shrinking projection method, Strong convergence\",\"abbrev_source_title\":\"J. Nonlinear Convex Anal.\",\"bibtex\":\"@ARTICLE{TXL_JNCA20_1,\\nauthor={Tan, Bing and Xu, Shanshan and Li, Songxiao},\\ntitle={Inertial hybrid and shrinking projection algorithms for solving variational inequality problems},\\njournal={Journal of Nonlinear and Convex Analysis},\\nyear={2020},\\nvolume={21},\\nnumber={10},\\npages={2193--2206},\\nurl={https://bingtan.me/files/paper/TXL-JNCA2020-10.pdf},\\nabstract={In this paper, we propose two inertial hybrid and shrinking projection algorithms for strict pseudo-contractions in Hilbert spaces and obtain strong theorems in general conditions. In addition, we also propose two new inertial hybrid and shrinking projection algorithms without extrapolating step for non-expansive mappings in Hilbert spaces and get strong convergence results. Finally, we give some numerical examples to illustrate the computational performance of our proposed algorithms.},\\nkeywords={Variational inequality problem,  Inertial method, Hybrid projection method, Shrinking projection method, Strong convergence},\\nabbrev_source_title={J. Nonlinear Convex Anal.},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Xu, S.\",\"Li, S.\"],\"key\":\"TXL_JNCA20_1\",\"id\":\"TXL_JNCA20_1\",\"bibbaseid\":\"tan-xu-li-inertialhybridandshrinkingprojectionalgorithmsforsolvingvariationalinequalityproblems-2020\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TXL-JNCA2020-10.pdf\"},\"keyword\":[\"Variational inequality problem\",\"Inertial method\",\"Hybrid projection method\",\"Shrinking projection method\",\"Strong convergence\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Xu\"],\"firstnames\":[\"Shanshan\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Li\"],\"firstnames\":[\"Songxiao\"],\"suffixes\":[]}],\"title\":\"Modified inertial hybrid and shrinking projection algorithms for solving fixed point problems\",\"journal\":\"Mathematics\",\"year\":\"2020\",\"volume\":\"8\",\"number\":\"2\",\"doi\":\"10.3390/math8020236\",\"pages\":\"236\",\"url\":\"https://bingtan.me/files/paper/TXL-Math2020.pdf\",\"abstract\":\"In this paper, we introduce two modified inertial hybrid and shrinking projection algorithms for solving fixed point problems by combining the modified inertial Mann algorithm with the projection algorithm. We establish strong convergence theorems under certain suitable conditions. Finally, our algorithms are applied to convex feasibility problem, variational inequality problem, and location theory. The algorithms and results presented in this paper can summarize and unify corresponding results previously known in this field.\",\"keywords\":\"Conjugate gradient method, Hybrid projection method, Inertial method, Nonexpansive mapping, Shrinking projection method, Hybrid steepest descent method, Strong convergence\",\"abbrev_source_title\":\"Mathematics\",\"bibtex\":\"@ARTICLE{TXL_MATH20,\\nauthor={Tan, Bing and Xu, Shanshan and Li, Songxiao},\\ntitle={Modified inertial hybrid and shrinking projection algorithms for solving fixed point problems},\\njournal={Mathematics},\\nyear={2020},\\nvolume={8},\\nnumber={2},\\ndoi={10.3390/math8020236},\\npages={236},\\nurl={https://bingtan.me/files/paper/TXL-Math2020.pdf},\\nabstract={In this paper, we introduce two modified inertial hybrid and shrinking projection algorithms for solving fixed point problems by combining the modified inertial Mann algorithm with the projection algorithm. We establish strong convergence theorems under certain suitable conditions. Finally, our algorithms are applied to convex feasibility problem, variational inequality problem, and location theory. The algorithms and results presented in this paper can summarize and unify corresponding results previously known in this field.},\\nkeywords={Conjugate gradient method,  Hybrid projection method,  Inertial method,  Nonexpansive mapping,  Shrinking projection method,  Hybrid steepest descent method,  Strong convergence},\\nabbrev_source_title={Mathematics},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Xu, S.\",\"Li, S.\"],\"key\":\"TXL_MATH20\",\"id\":\"TXL_MATH20\",\"bibbaseid\":\"tan-xu-li-modifiedinertialhybridandshrinkingprojectionalgorithmsforsolvingfixedpointproblems-2020\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TXL-Math2020.pdf\"},\"keyword\":[\"Conjugate gradient method\",\"Hybrid projection method\",\"Inertial method\",\"Nonexpansive mapping\",\"Shrinking projection method\",\"Hybrid steepest descent method\",\"Strong convergence\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Zhou\"],\"firstnames\":[\"Zheng\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Li\"],\"firstnames\":[\"Songxiao\"],\"suffixes\":[]}],\"title\":\"Strong convergence of modified inertial mann algorithms for nonexpansive mappings\",\"journal\":\"Mathematics\",\"year\":\"2020\",\"volume\":\"8\",\"number\":\"4\",\"doi\":\"10.3390/math8040462\",\"pages\":\"462\",\"url\":\"https://bingtan.me/files/paper/TZL-Math2020.pdf\",\"abstract\":\"We investigated two new modified inertial Mann Halpern and inertial Mann viscosity algorithms for solving fixed point problems. Strong convergence theorems under some fewer restricted conditions are established in the framework of infinite dimensional Hilbert spaces. Finally, some numerical examples are provided to support our main results. The algorithms and results presented in this paper can generalize and extend corresponding results previously known in the literature.\",\"keywords\":\"Halpern method, Inertial method, Nonexpansive mapping, Strong convergence, Viscosity method\",\"abbrev_source_title\":\"Mathematics\",\"bibtex\":\"@ARTICLE{TZL_MATH20,\\nauthor={Tan, Bing and Zhou, Zheng and Li, Songxiao},\\ntitle={Strong convergence of modified inertial mann algorithms for nonexpansive mappings},\\njournal={Mathematics},\\nyear={2020},\\nvolume={8},\\nnumber={4},\\ndoi={10.3390/math8040462},\\npages={462},\\nurl={https://bingtan.me/files/paper/TZL-Math2020.pdf},\\nabstract={We investigated two new modified inertial Mann Halpern and inertial Mann viscosity algorithms for solving fixed point problems. Strong convergence theorems under some fewer restricted conditions are established in the framework of infinite dimensional Hilbert spaces. Finally, some numerical examples are provided to support our main results. The algorithms and results presented in this paper can generalize and extend corresponding results previously known in the literature.},\\nkeywords={Halpern method,  Inertial method,  Nonexpansive mapping,  Strong convergence,  Viscosity method},\\nabbrev_source_title={Mathematics},\\n}\\n\\n\",\"author_short\":[\"Tan, B.\",\"Zhou, Z.\",\"Li, S.\"],\"key\":\"TZL_MATH20\",\"id\":\"TZL_MATH20\",\"bibbaseid\":\"tan-zhou-li-strongconvergenceofmodifiedinertialmannalgorithmsfornonexpansivemappings-2020\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/TZL-Math2020.pdf\"},\"keyword\":[\"Halpern method\",\"Inertial method\",\"Nonexpansive mapping\",\"Strong convergence\",\"Viscosity method\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Liu\"],\"firstnames\":[\"Liya\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Cho\"],\"firstnames\":[\"Sun\",\"Y.\"],\"suffixes\":[]}],\"title\":\"On the resolution of variational inequality problems with a double-hierarchical structure\",\"journal\":\"Journal of Nonlinear and Convex Analysis\",\"year\":\"2020\",\"volume\":\"21\",\"number\":\"2\",\"pages\":\"377–386\",\"url\":\"https://bingtan.me/files/paper/LTC-JNCA2020.pdf\",\"abstract\":\"In this paper, we discuss a pseudo-monotone variational inequality problem with a variational inequality constraint over a general, nonempty, closed and convex set, which is called the double-hierarchical constrained optimization problem. In addition, we propose an iterative algorithm by incorporating inertial terms in the extragradient algorithm. Strong convergence of the algorithm to the unique solution of the problem is guaranteed under certain assumptions.\",\"keywords\":\"Constrained optimization problem, Inertial method, Pseudomonotone operator, Variational inequality problem\",\"abbrev_source_title\":\"J. Nonlinear Convex Anal.\",\"bibbase_note\":\"<span style=\\\"color: red\\\">(ESI Highly Cited Paper)</span>\",\"bibtex\":\"@ARTICLE{LTC_JNCA20,\\nauthor={Liu, Liya and Tan, Bing and Cho, Sun Y.},\\ntitle={On the resolution of variational inequality problems with a double-hierarchical structure},\\njournal={Journal of Nonlinear and Convex Analysis},\\nyear={2020},\\nvolume={21},\\nnumber={2},\\npages={377--386},\\nurl={https://bingtan.me/files/paper/LTC-JNCA2020.pdf},\\nabstract={In this paper, we discuss a pseudo-monotone variational inequality problem with a variational inequality constraint over a general, nonempty, closed and convex set, which is called the double-hierarchical constrained optimization problem. In addition, we propose an iterative algorithm by incorporating inertial terms in the extragradient algorithm. Strong convergence of the algorithm to the unique solution of the problem is guaranteed under certain assumptions.},\\nkeywords={Constrained optimization problem,  Inertial method, Pseudomonotone operator,  Variational inequality problem},\\nabbrev_source_title={J. Nonlinear Convex Anal.},\\nbibbase_note={<span style=\\\"color: red\\\">(ESI Highly Cited Paper)</span>},\\n}\\n\\n\",\"author_short\":[\"Liu, L.\",\"Tan, B.\",\"Cho, S. Y.\"],\"key\":\"LTC_JNCA20\",\"id\":\"LTC_JNCA20\",\"bibbaseid\":\"liu-tan-cho-ontheresolutionofvariationalinequalityproblemswithadoublehierarchicalstructure-2020\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/LTC-JNCA2020.pdf\"},\"keyword\":[\"Constrained optimization problem\",\"Inertial method\",\"Pseudomonotone operator\",\"Variational inequality problem\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Zhou\"],\"firstnames\":[\"Zheng\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Li\"],\"firstnames\":[\"Songxiao\"],\"suffixes\":[]}],\"title\":\"A new accelerated self-adaptive stepsize algorithm with excellent stability for split common fixed point problems\",\"journal\":\"Computational and Applied Mathematics\",\"year\":\"2020\",\"volume\":\"39\",\"number\":\"3\",\"doi\":\"10.1007/s40314-020-01237-0\",\"pages\":\"220\",\"url\":\"https://bingtan.me/files/paper/ZTL-COAM2020.pdf\",\"abstract\":\"In the framework of Hilbert spaces, we study the solutions of split common fixed point problems. A new accelerated self-adaptive stepsize algorithm with excellent stability is proposed under the effects of inertial techniques and Meir–Keeler contraction mappings. The strong convergence theorems are obtained without prior knowledge of operator norms. Finally, in applications, our main results in this paper are applied to signal recovery problems.\",\"keywords\":\"Inertial method, Meir–Keeler contraction, Adaptive stepsize, Signal processing problem, Split common fixed point problem\",\"abbrev_source_title\":\"Comput. Appl. Math.\",\"bibtex\":\"@ARTICLE{ZTL_COAM20,\\nauthor={Zhou, Zheng and Tan, Bing and Li, Songxiao},\\ntitle={A new accelerated self-adaptive stepsize algorithm with excellent stability for split common fixed point problems},\\njournal={Computational and Applied Mathematics},\\nyear={2020},\\nvolume={39},\\nnumber={3},\\ndoi={10.1007/s40314-020-01237-0},\\npages={220},\\nurl={https://bingtan.me/files/paper/ZTL-COAM2020.pdf},\\nabstract={In the framework of Hilbert spaces, we study the solutions of split common fixed point problems. A new accelerated self-adaptive stepsize algorithm with excellent stability is proposed under the effects of inertial techniques and Meir–Keeler contraction mappings. The strong convergence theorems are obtained without prior knowledge of operator norms. Finally, in applications, our main results in this paper are applied to signal recovery problems.},\\nkeywords={Inertial method,  Meir–Keeler contraction,  Adaptive stepsize,  Signal processing problem, Split common fixed point problem},\\nabbrev_source_title={Comput. Appl. Math.},\\n}\\n\\n\",\"author_short\":[\"Zhou, Z.\",\"Tan, B.\",\"Li, S.\"],\"key\":\"ZTL_COAM20\",\"id\":\"ZTL_COAM20\",\"bibbaseid\":\"zhou-tan-li-anewacceleratedselfadaptivestepsizealgorithmwithexcellentstabilityforsplitcommonfixedpointproblems-2020\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/ZTL-COAM2020.pdf\"},\"keyword\":[\"Inertial method\",\"Meir–Keeler contraction\",\"Adaptive stepsize\",\"Signal processing problem\",\"Split common fixed point problem\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Zhou\"],\"firstnames\":[\"Zheng\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Li\"],\"firstnames\":[\"Songxiao\"],\"suffixes\":[]}],\"title\":\"An inertial shrinking projection algorithm for split common fixed point problems\",\"journal\":\"Journal of Applied Analysis and Computation\",\"year\":\"2020\",\"volume\":\"10\",\"number\":\"5\",\"pages\":\"2104–2120\",\"doi\":\"10.11948/20190330\",\"url\":\"https://bingtan.me/files/paper/ZTL-JAAC2020.pdf\",\"abstract\":\"In this paper, the purpose is to introduce and study a new modified shrinking projection algorithm with inertial effects, which solves split common fixed point problems in Banach spaces. The corresponding strong convergence theorems are obtained without the assumption of semi-compactness on map-pings. Finally, some numerical examples are presented to illustrate the results in this paper.\",\"keywords\":\"Inertial method, Shrinking projection method, Split common fixed point problem, Strong convergence\",\"abbrev_source_title\":\"J. Appl. Anal. Comput.\",\"bibtex\":\"@ARTICLE{ZTL_JAAC20,\\nauthor={Zhou, Zheng and Tan, Bing and Li, Songxiao},\\ntitle={An inertial shrinking projection algorithm for split common fixed point problems},\\njournal={Journal of Applied Analysis and Computation},\\nyear={2020},\\nvolume={10},\\nnumber={5},\\npages={2104--2120},\\ndoi={10.11948/20190330},\\nurl={https://bingtan.me/files/paper/ZTL-JAAC2020.pdf},\\nabstract={In this paper, the purpose is to introduce and study a new modified shrinking projection algorithm with inertial effects, which solves split common fixed point problems in Banach spaces. The corresponding strong convergence theorems are obtained without the assumption of semi-compactness on map-pings. Finally, some numerical examples are presented to illustrate the results in this paper.},\\nkeywords={Inertial method,  Shrinking projection method,  Split common fixed point problem,  Strong convergence},\\nabbrev_source_title={J. Appl. Anal. Comput.},\\n}\\n\\n\",\"author_short\":[\"Zhou, Z.\",\"Tan, B.\",\"Li, S.\"],\"key\":\"ZTL_JAAC20\",\"id\":\"ZTL_JAAC20\",\"bibbaseid\":\"zhou-tan-li-aninertialshrinkingprojectionalgorithmforsplitcommonfixedpointproblems-2020\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/ZTL-JAAC2020.pdf\"},\"keyword\":[\"Inertial method\",\"Shrinking projection method\",\"Split common fixed point problem\",\"Strong convergence\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Luo\"],\"firstnames\":[\"Yinglin\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Shang\"],\"firstnames\":[\"Meijuan\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Tan\"],\"firstnames\":[\"Bing\"],\"suffixes\":[]}],\"title\":\"A general inertial viscosity type method for nonexpansive mappings and its applications in signal processing\",\"journal\":\"Mathematics\",\"year\":\"2020\",\"volume\":\"8\",\"number\":\"2\",\"doi\":\"10.3390/math8020288\",\"pages\":\"288\",\"url\":\"https://bingtan.me/files/paper/LST-Math2020.pdf\",\"abstract\":\"In this paper, we propose viscosity algorithms with two different inertia parameters for solving fixed points of nonexpansive and strictly pseudocontractive mappings. Strong convergence theorems are obtained in Hilbert spaces and the applications to the signal processing are considered. Moreover, some numerical experiments of proposed algorithms and comparisons with existing algorithms are given to the demonstration of the efficiency of the proposed algorithms. The numerical results show that our algorithms are superior to some related algorithms.\",\"keywords\":\"Inclusion problem, Nonexpansive mapping, Signal processing problem, Strict pseudo-contraction, Variational inequality problem\",\"abbrev_source_title\":\"Mathematics\",\"bibtex\":\"@ARTICLE{LST_MATH20,\\nauthor={Luo, Yinglin and Shang, Meijuan and Tan, Bing},\\ntitle={A general inertial viscosity type method for nonexpansive mappings and its applications in signal processing},\\njournal={Mathematics},\\nyear={2020},\\nvolume={8},\\nnumber={2},\\ndoi={10.3390/math8020288},\\npages={288},\\nurl={https://bingtan.me/files/paper/LST-Math2020.pdf},\\nabstract={In this paper, we propose viscosity algorithms with two different inertia parameters for solving fixed points of nonexpansive and strictly pseudocontractive mappings. Strong convergence theorems are obtained in Hilbert spaces and the applications to the signal processing are considered. Moreover, some numerical experiments of proposed algorithms and comparisons with existing algorithms are given to the demonstration of the efficiency of the proposed algorithms. The numerical results show that our algorithms are superior to some related algorithms.},\\nkeywords={Inclusion problem,  Nonexpansive mapping,  Signal processing problem,  Strict pseudo-contraction,  Variational inequality problem},\\nabbrev_source_title={Mathematics},\\n}\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\",\"author_short\":[\"Luo, Y.\",\"Shang, M.\",\"Tan, B.\"],\"key\":\"LST_MATH20\",\"id\":\"LST_MATH20\",\"bibbaseid\":\"luo-shang-tan-ageneralinertialviscositytypemethodfornonexpansivemappingsanditsapplicationsinsignalprocessing-2020\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://bingtan.me/files/paper/LST-Math2020.pdf\"},\"keyword\":[\"Inclusion problem\",\"Nonexpansive mapping\",\"Signal processing problem\",\"Strict pseudo-contraction\",\"Variational inequality problem\"],\"metadata\":{\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\"html\":\"\"}],\n      metadata: {\"owner\":\"tan, b\",\"authorlinks\":{\"tan, b\":\"https://bingtan.me/pubs_author.html\"}},\n      ownerID: \"7E3FLjQkhAtTfnTdh\"\n    };\n  </script>\n\n  <script type=\"text/javascript\">\n  var site$;\n  if (typeof $ != 'undefined') {\n    console.log('existing jquery: storing and then restoring');\n    site$ = $;\n    $ = null;\n  }\n  </script>\n\n  <script src=\"https://ajax.googleapis.com/ajax/libs/jquery/2.2.4/jquery.min.js\">\n  </script>\n  <script type=\"text/javascript\">\n  if (site$) {\n    console.log('existing jquery: avoiding conflict and restoring');\n    bb$ = $.noConflict(true);\n    $ = site$;\n  } else {\n    bb$ = $;\n  }\n  </script>\n\n  <script src=\"//bibbase.org/js/bibbase.min.js\"\n          type=\"text/javascript\">\n  </script>\n\n  <script type=\"text/javascript\"\n          src=\"https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML\">\n  </script>\n  <script type=\"text/x-mathjax-config\">\n    MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$'], ['\\\\(','\\\\)']]},\n                        skipTags: [\"body\"],\n                        processClass: \"bibbase_paper\"});\n  </script>\n\n  <style>\n  @media print {\n    .dontprint {\n        display: none !important;\n    }\n\n  .bibbase_group {\n    background-color: #E0E0E0;\n    font-style: italic;\n    font-size: larger;\n    text-shadow: 0px 0px 3px #FFFFFF;\n    border-radius: 4px 4px 4px 4px;\n    -moz-border-radius: 4px 4px 4px 4px;\n    -webkit-border-radius: 4px;\n    padding: 5px 40px 5px;\n    margin-top: 10px;\n    margin-bottom: 5px;\n    cursor: pointer;\n  }\n\n  .bibbase_paper {\n    margin-bottom: 5px;\n  }\n\n  }\n  </style>\n\n  \n  <div style=\"float: right; margin-right: 10px; margin-top: 10px; text-align: right; font-size: 12px\">\n    generated by\n    <a href=\"//bibbase.org\"\n       onclick=\"trackOutboundLink('bibbase', 'logo clicked', window.location.href, '//bibbase.org'); return false;\">\n      <img src=\"//bibbase.org/img/logo.svg\"\n           style=\"vertical-align: middle; margin-left: 3px; height: 16px;\"/\n           alt=\"bibbase.org\"\n           title=\"BibBase – The easiest way to maintain your publications page.\"\n        ></a>\n    \n  </div>\n  \n\n  <div id=\"bibbase_header\" class=\"dontprint\" style=\"\">\n\n    <ul class=\"nav nav-pills\" style=\"margin: 0px;\">\n\n      <li class=\"dropdown\" id=\"groupby_dropdown\">\n      <a class=\"dropdown-toggle\"\n         data-toggle=\"dropdown\"\n         href=\"#\">\n          Group by\n          <b class=\"caret\"></b>\n      </a>\n      <ul class=\"dropdown-menu\">\n        <li class=\"groupby year\"><a onclick=\"groupby('year')\">\n            Year</a>\n        </li>\n        <li class=\"groupby author\"><a onclick=\"groupby('author_short')\">\n            Author</a>\n        </li>\n        <li class=\"groupby type\"><a onclick=\"groupby('type')\">\n            Type</a>\n        </li>\n        <li class=\"groupby keyword\"><a onclick=\"groupby('keyword')\">\n            Keyword</a>\n        </li>\n        <li class=\"groupby downloads\"><a onclick=\"groupby('downloads')\">\n            Downloads</a>\n        </li>\n      </ul>\n      </li>\n\n\n      <li class=\"dropdown\" id=\"menu_dropdown\">\n      <a class=\"dropdown-toggle\"\n         data-toggle=\"dropdown\"\n         href=\"#\" alt=\"controls\">\n          <i class=\"fa fa-reorder\" alt=\"controls\"></i>\n          <b class=\"caret\"></b>\n      </a>\n      <ul class=\"dropdown-menu\">\n        <li>\n          <a onclick=\"toggleAll()\">\n            <i class=\"fa fa-chevron-down fa-fw\"></i> Expand/Collapse All\n          </a>\n        </li>\n        <li>\n          <a download=\"scopus.bib\" href=\"data:text/bibtex;base64,@ARTICLE{TQW_NUMA24,
author={Tan, Bing and Qin, Xiaolong and Wang, Xianfu},
title={Alternated inertial algorithms for split feasibility problems},
journal={Numerical Algorithms},
year={2024},
volume={95},
number={2},
pages={773--812},
doi={10.1007/s11075-023-01589-8},
url={https://bingtan.me/files/paper/TQW-NUMA2024.pdf},
abstract={We introduce four novel relaxed CQ algorithms with alternating inertial for solving split feasibility problems in real Hilbert spaces. The proposed algorithms employ a new non-monotonic adaptive step size criterion and utilize two different step sizes in each iteration. The weak convergence of the iterative sequences generated by the proposed algorithms is established under some weak conditions. Moreover, the Fejér monotonicity of the even subsequence with respect to the solution set is recovered. Two applications in signal denoising and image deblurring are given to illustrate the computational efficiency of our algorithms.},
keywords={Split feasibility problem,  CQ method,  Projection and contraction method,  Alternated inertial method,  Signal processing,  Image restoration},
abbrev_source_title={Numer. Algorithms},
}



@ARTICLE{XCT_OPT24,
author={Xie, Zhongbing and Cai, Gang and Tan, Bing},
title={Inertial subgradient extragradient method for solving pseudomonotone equilibrium probelms and fixed point problems in Hilbert spaces},
journal={Optimization},
year={2024},
volume={73},
number={5},
pages={1329-1354},
doi={10.1080/02331934.2022.2157677},
url={https://bingtan.me/files/paper/XCT-OPT2024.pdf},
abstract={This paper proposes a new inertial subgradient extragradient method for solving equilibrium problems with pseudomonotone and Lipschitz-type bifunctions and fixed point problems for nonexpansive mappings in real Hilbert spaces. Precisely, we prove that the sequence generated by proposed algorithm converges strongly to a common solution of equilibrium problems and fixed point problems. We use an effective self-adaptive step size rule to accelerate the convergence process of our proposed iterative algorithm. Moreover, some numerical results are given to show the effectiveness of the proposed algorithm. The results obtained in this paper extend and improve many recent ones in the literature.},
keywords={Inertial method,  Subgradient extragradient method, Equilibrium probelm, Fixed point problem, Strong convergence},
abbrev_source_title={Optimization},
}



@ARTICLE{TQ_AMSA23,
author={Tan, Bing and Qin, Xiaolong},
title={An alternated inertial algorithm with weak and linear convergence for solving monotone inclusions},
journal={Annals of Mathematical Sciences and Applications},
year={2023},
volume={8},
number={2},
pages={321--345},
doi={10.4310/AMSA.2023.v8.n2.a7},
url={https://bingtan.me/files/paper/TQ-AMSA2023.pdf},
abstract={Inertial-based methods have the drawback of not preserving the Fejér monotonicity of iterative sequences, which may result in slower convergence compared to their corresponding non-inertial versions. To overcome this issue, Mu and Peng [Stat. Optim. Inf. Comput. 3 (2015), 241–248; MR3393305] suggested an alternating inertial method that can recover the Fejér monotonicity of even subsequences. In this paper, we propose a modified version of the forward-backward algorithm with alternating inertial and relaxation effects to solve an inclusion problem in real Hilbert spaces. The weak and linear convergence of the presented algorithm is established under suitable and mild conditions on the involved operators and parameters. Furthermore, the Fejér monotonicity of even subsequences generated by the proposed algorithm with respect to the solution set is recovered. Finally, our tests on image restoration problems demonstrate the superiority of the proposed algorithm over some related results.},
keywords={Inclusion problems, Alternated inertial, Forward-backward method, Tseng's method, Projection and contraction method, Linear convergence},
abbrev_source_title={Ann. Math. Sci. Appl.},
}



@ARTICLE{TGQ_PAFA23,
author={Tan, Bing and Qin, Xiaolong and Gibali, Aviv},
title={Three approximation methods for solving constraint variational inequalities and related problems},
journal={Pure and Applied Functional Analysis},
year={2023},
volume={8},
number={3},
pages={965--986},
url={https://bingtan.me/files/paper/TGQ_PAFA2023.pdf},
abstract={In this paper, we present three new self-adaptive one-projection algorithms to find common solutions for the pseudo-monotone variational inequality problem and the fixed point problem of a demi-contractive mapping. Note that the suggested approaches use a non-monotonic self-adaptive step size so that they can work well without knowing the prior knowledge of the Lipschitz constant of the mapping. Strong convergence theorems of the proposed iterative schemes are established in real Hilbert spaces. Several mathematical experiments are reported to demonstrate the numerical behavior of the suggested algorithms and compare them with the existing ones. Finally, the suggested methods are used to solve optimal control problems.},
keywords={Variational inequality, Fixed point, Extragradient method, Hybrid steepest descent method, Pseudomonotone mapping},
abbrev_source_title={Pure Appl. Funct. Anal.},
}



@ARTICLE{TLC_AA23,
author={Tan, Bing and Li, Songxiao and Cho, Sun Y.},
title={Inertial projection and contraction methods for pseudomonotone variational inequalities with non-Lipschitz operators and applications},
journal={Applicable Analysis},
year={2023},
volume={102},
number={4},
doi={10.1080/00036811.2021.1979219},
pages={1199--1221},
url={https://bingtan.me/files/paper/TLC-AA2023.pdf},
abstract={In this paper, some new accelerated iterative schemes are proposed to solve the variational inequality problem with a pseudomonotone and uniformly continuous operator in real Hilbert spaces. Strong convergence theorems of the suggested algorithms are obtained without the prior knowledge of the Lipschitz constant of the operator. Some numerical experiments and applications are performed to illustrate the advantages of the proposed methods with respect to several related ones.},
keywords={Inertial extragradient method,  Projection and contraction method,  Pseudomonotone operator,  Non-Lipschitz operator,  Variational inequality problem},
abbrev_source_title={Appl. Anal.},
}



@ARTICLE{TSCC_IJCM23,
author={Tan, Bing and Sunthrayuth, Pongsakorn and Cholamjiak, Prasit and  Cho, Yeol J.},
title={Modified inertial extragradient methods for finding minimum-norm solution of the variational inequality problem with applications to optimal control problem},
journal={International Journal of Computer Mathematics},
year={2023},
volume={100},
number={3},
pages={525--545},
doi={10.1080/00207160.2022.2137672},
url={https://bingtan.me/files/paper/TSCC-IJCM23.pdf},
abstract={In order to discover the minimum-norm solution of the pseudomonotone variational inequality problem in a real Hilbert space, we provide two variants of the inertial extragradient approach with a novel generalized adaptive step size. Two of the suggested algorithms make use of the projection and contraction methods. We demonstrate several strong convergence findings without requiring the prior knowledge of the Lipschitz constant of the mapping. Finally, we give a number of numerical examples that highlight the benefits and effectiveness of the suggested algorithms and how they may be used to solve the optimal control problem.},
keywords={Variational inequality problem, Optimal control problem, Inertial method, Projection and contraction method},
abbrev_source_title={Int. J. Comput. Math.},
}



@ARTICLE{TL_JIMO23,
author={Tan, Bing and Li, Songxiao},
title={Adaptive inertial subgradient extragradient methods for finding minimum-norm solutions of pseudomonotone variational inequalities},
journal={Journal of Industrial and Management Optimization},
year={2023},
volume={19},
number={10},
pages={7640--7659},
doi={10.3934/jimo.2022060},
url={https://bingtan.me/files/paper/TL-JIMO2023.pdf},
abstract={In this paper, four modified inertial subgradient extragradient methods with a new non-monotonic step size criterion are investigated for pseudomonotone variational inequality problems in real Hilbert spaces. Our algorithms employ two different step sizes in each iteration to update the values of iterative sequences, and they work well without the prior information about the Lipschitz constant of the operator. Strong convergence theorems of the proposed iterative schemes are established under some suitable and mild conditions. Some numerical examples are provided to demonstrate the computational efficiency and advantages of the proposed methods over other known ones.},
keywords={Variational inequality problem, Inertial method, Extragradient method, Pseudomonotone operator, Non-Lipschitz operator},
abbrev_source_title={J. Ind. Manag. Optim.},
}



@ARTICLE{ZTL_MMAS23,
author={Zhou, Zheng and Tan, Bing and Li, Songxiao},
title={Inertial algorithms with adaptive stepsizes for split variational inclusion problems and their applications to signal recovery problem},
journal={Mathematical Methods in the Applied Sciences},
year={2023},
volume={doi:10.1002/mma.9436},
doi={10.1002/mma.9436},
url={https://bingtan.me/files/paper/ZTL-MMAS2023.pdf},
abstract={With the help of the Meir-Keeler contraction method and the Mann-type method, two adaptive inertial iterative schemes are introduced for finding solutions of the split variational inclusion problem in Hilbert spaces. The strong convergence of the suggested algorithms is guaranteed by a new stepsize criterion that does not require calculation of the bounded linear operator norm. Some numerical experiments and applications in signal recovery problems are given to demonstrate the efficiency of the proposed algorithms.},
keywords={Adaptive stepsize, Inertial method, Mann method, Meir-Keeler contraction, Signal recovery, Split variational inclusion problem},
abbrev_source_title={Math. Methods Appl. Sci.},
}



@ARTICLE{LTL_OPT23,
author={Luo, Yinglin and Tan, Bing and Li, Songxiao},
title={Inertial splitting algorithms for nonlinear operators of pseudocontractive and accretive types},
journal={Optimization},
year={2023},
volume={72},
number={3},
pages={647--675},
doi={10.1080/02331934.2021.1981896},
url={https://bingtan.me/files/paper/LTL-OPT2023.pdf},
abstract={In this paper, inertial splitting algorithms for nonlinear operators of pseudocontractive and accretive types are proposed. Weak and strong convergence theorems are established in uniformly convex and $q$-uniformly smooth Banach spaces. Numerical examples are given to illustrate the effectiveness of our proposed algorithms.},
keywords={Accretive operator,  Banach space,  Inertial method,  Strict pseudo-contraction,  Strong convergence},
abbrev_source_title={Optimization},
}



@ARTICLE{ZCTD_NUMA23,
author={Zhou, Xiaolin and Cai, Gang and Tan, Bing and Dong, Qiao L.},
title={A modified generalized version of projected reflected gradient method in Hilbert spaces},
journal={Numerical Algorithms},
year={2023},
volume={doi:10.1007/s11075-023-01566-1},
doi={10.1007/s11075-023-01566-1},
url={https://bingtan.me/files/paper/ZCTD-NUMA2023.pdf},
abstract={This article is concerned with a universal version of projected reflected gradient method with new step size for solving variational inequality problem in Hilbert spaces. Under appropriate assumptions controlled by the operators and parameters, we acquire the weak convergence of the proposed algorithm. We establish an R-linear convergence rate of our method on the condition that the relevant mapping is strongly monotone. We rework our first algorithm so that it can be simplified to several generalized methods in the literature. The efficacy and availability of our proposed iterative scheme are demonstrated in numerical experiments.},
keywords={Projected reflected gradient method, Variational inequality, Weak and linear convergence, Hilbert spaces},
abbrev_source_title={Numer. Algorithms},
}



@ARTICLE{HWTW_JIMO23,
author={Hu, Shaotao and Wang, Yuanheng and Tan, Bing and Wang, Fenghui},
title={Inertial iterative method for solving variational inequality problems of pseudo-monotone operators and fixed point problems of nonexpansive mappings in {H}ilbert spaces},
journal={Journal of Industrial and Management Optimization},
year={2023},
volume={19},
number={4},
pages={2655--2675},
doi={10.3934/jimo.2022060},
url={https://bingtan.me/files/paper/HWTW-JIMO2023.pdf},
abstract={In this paper, we propose a new inertial viscosity iterative algorithm for solving the variational inequality problem with a pseudo-monotone operator and the fixed point problem involving a nonexpansive mapping in real Hilbert spaces. The advantage of the proposed algorithm is that it can work without the prior knowledge of the Lipschitz constant of the mapping. The strong convergence of the sequence generated by the proposed algorithm is proved under some suitable assumptions imposed on the parameters. Some numerical experiments are given to support our main results.},
keywords={Inertial method,  Viscosity method,  Strong convergence, Variational inequality problem, Fixed point problem, Nonexpansive mapping, Pseudomonotone operator},
abbrev_source_title={J. Ind. Manag. Optim.},
}



@ARTICLE{TQC_NUMA22,
author={Tan, Bing and Qin, Xiaolong and Cho, Sun Y.},
title={Revisiting subgradient extragradient methods for solving variational inequalities},
journal={Numerical Algorithms},
year={2022},
volume={90},
number={4},
pages={1593--1615},
doi={10.1007/s11075-021-01243-1},
url={https://bingtan.me/files/paper/TQC-NUMA2022.pdf},
abstract={In this paper, several extragradient algorithms with inertial effects and adaptive non-monotonic step sizes are proposed to solve pseudomonotone variational inequalities in real Hilbert spaces. The strong convergence of the proposed methods is established without the prior knowledge of the Lipschitz constant of the mapping. Some numerical experiments are given to illustrate the advantages and efficiency of the proposed schemes over previously known ones.},
keywords={Armijo stepsize,  Inertial extragradient method,  Non-Lipschitz operator,  Pseudomonotone operator,  Variational inequality problem},
abbrev_source_title={Numer. Algorithms},
}



@ARTICLE{TQY_JOGO22,
author={Tan, Bing and Qin, Xiaolong and Yao, Jen C.},
title={Strong convergence of inertial projection and contraction methods for pseudomonotone variational inequalities with applications to optimal control problems},
journal={Journal of Global Optimization},
year={2022},
volume={82},
number={3},
pages={523--557},
doi={10.1007/s10898-021-01095-y},
url={https://bingtan.me/files/paper/TQY-JOGO2022.pdf},
abstract={This paper investigates some inertial projection and contraction methods for solving pseudomonotone variational inequality problems in real Hilbert spaces. The algorithms use a new non-monotonic step size so that they can work without the prior knowledge of the Lipschitz constant of the operator. Strong convergence theorems of the suggested algorithms are obtained under some suitable conditions. Some numerical experiments in finite- and infinite-dimensional spaces and applications in optimal control problems are implemented to demonstrate the performance of the suggested schemes and we also compare them with several related results.},
keywords={Inertial method,  Optimal control problem,  Projection and contraction method,  Pseudomonotone operator,  Subgradient extragradient method,  Variational inequality problem},
abbrev_source_title={J. Global Optim.},
}



@ARTICLE{TQ_AMP22,
author={Tan, Bing and Qin, Xiaolong},
title={Modified inertial projection and contraction algorithms for solving variational inequality problems with non-Lipschitz continuous operators},
journal={Analysis and Mathematical Physics},
year={2022},
volume={12},
number={1},
doi={10.1007/s13324-021-00638-6},
pages={26},
url={https://bingtan.me/files/paper/TQ-AMP2022.pdf},
abstract={In this paper, we present four modified inertial projection and contraction methods to solve the variational inequality problem with a pseudo-monotone and non-Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems of the proposed algorithms are established without the prior knowledge of the Lipschitz constant of the operator. Several numerical experiments and the applications to optimal control problems are provided to verify the advantages and efficiency of the proposed algorithms.},
keywords={Inertial method,  Projection and contraction method,  Pseudomonotone operator,  Subgradient extragradient method,  Non-Lipschitz operator,  Variational inequality problem},
abbrev_source_title={Anal. Math. Phys.},
}



@ARTICLE{TPQY_FPT22,
author={Tan, Bing and Petruşel, Adrian and Qin, Xiaolong and Yao, Jen C.},
title={Global and linear convergence of alternated inertial single projection algorithms for pseudo-monotone variational inequalities},
journal={Fixed Point Theory},
year={2022},
volume={23},
number={1},
pages={391--426},
doi={10.24193/fpt-ro.2022.1.25},
url={https://bingtan.me/files/paper/TPQY-FPT2022.pdf},
abstract={In this paper, we investigate three new relaxed single projection methods with alternating inertial extrapolation steps and adaptive non-monotonic step sizes for solving pseudo-monotone variational inequalities in real Hilbert spaces. The proposed algorithms need to compute the projection on the feasible set only once in each iteration and they can work adaptively without the prior information of the Lipschitz constant of the mapping. The weak convergence theorems of the proposed iterative schemes are established under some appropriate conditions imposed on the parameters. These methods recover the Fejér monotonicity of the even subsequence with respect to the solution and obtain linear convergence rates. Finally, some numerical experiments and applications to optimal control problems are provided to demonstrate the advantages and efficiency of the proposed methods compared to some recent related ones.},
keywords={Adaptive stepsize,  Alternated inertial method,  Projection and contraction method,  Pseudomonotone operator,  Subgradient extragradient method,  Variational inequality problem},
abbrev_source_title={Fixed Point Theory},
}



@ARTICLE{TQ_JANO22,
author={Tan, Bing and Qin, Xiaolong},
title={Adaptive modified inertial projection and contraction methods for pseudomonotone variational inequalities},
journal={Journal of Applied and Numerical Optimization},
year={2022},
volume={4},
number={2},
pages={221--243},
doi={10.23952/jano.4.2022.2.08},
url={https://bingtan.me/files/paper/TQ-JANO2022.pdf},
abstract={To handle pseudomonotone variational inequality problems in real Hilbert spaces, four modified inertial projection and contraction algorithms with non-monotonic step sizes are suggested in this paper. The proposed algorithms take advantage of a novel non-monotonic step size criteria, allowing them to work without previous knowledge of the Lipschitz constant of the mapping involved. Under certain situations, the strong convergence of the iterative sequences generated by the suggested algorithms is established. Finally, several numerical experiments are offered to validate the theoretical conclusions.},
keywords={Inertial method, Pseudomonotone operator, Projection and contraction method, Subgradient extragradient method, Variational inequality problem},
abbrev_source_title={J. Appl. Numer. Optim.},
}



@ARTICLE{TQ_MMA22,
author={Tan, Bing and Qin, Xiaolong},
title={Self adaptive viscosity-type inertial extragradient algorithms for solving variational inequalities with applications},
journal={Mathematical Modelling and Analysis},
year={2022},
volume={27},
number={1},
pages={41--58},
doi={10.3846/mma.2022.13846},
url={https://bingtan.me/files/paper/TQ-MMA2022.pdf},
abstract={In this paper, we introduce two new inertial extragradient algorithms with non-monotonic stepsizes for solving monotone and Lipschitz continuous variational inequality problems in real Hilbert spaces. Strong convergence theorems of the suggested iterative schemes are established without the prior knowledge of the Lipschitz constant of the mapping. Finally, some numerical examples are provided to illustrate the efficiency and advantages of the proposed algorithms and compare them with some related ones.},
keywords={Inertial method, Subgradient extragradient method,  Tseng's extragradient method,  Optimal control problem,  Variational inequality problem,  Viscosity method},
abbrev_source_title={Math. Model. Anal.},
bibbase_note={<span style="color: red">(<s>ESI Highly Cited Paper</s>)</span>},
}



@ARTICLE{TLQ_FPT22,
author={Tan, Bing and Liu, Liya and Qin, Xiaolong},
title={Strong convergence of inertial extragradient algorithms for solving variational inequalities and fixed point problems},
journal={Fixed Point Theory},
year={2022},
volume={23},
number={2},
pages={707--728},
doi={10.24193/fpt-ro.2022.2.17},
url={https://bingtan.me/files/paper/TLQ-FPT2022.pdf},
abstract={This paper investigates two inertial extragradient algorithms for seeking a common solution to a variational inequality problem involving a monotone and Lipschitz continuous mapping and a fixed point problem with a demicontractive mapping in real Hilbert spaces. Our algorithms need to calculate the projection on the feasible set only once in each iteration. Moreover, they can work well without the prior information of the Lipschitz constant of the operator and do not contain any linesearch process. Strong convergence theorems of the suggested algorithms are established under suitable conditions. Some experiments are presented to illustrate the numerical efficiency of the suggested algorithms and compare them with some existing ones.},
keywords={Variational inequality problem, Fixed point problem, Subgradient extragradient method, Tseng's extragradient method, Inertial method, Demicontractive mapping},
abbrev_source_title={Fixed Point Theory},
}



@ARTICLE{TL_OPT22,
author={Tan, Bing and Li, Songxiao},
title={Modified inertial projection and contraction algorithms with non-monotonic step sizes for solving variational inequalities and their applications},
journal={Optimization},
year={2022},
volume={doi:10.1080/02331934.2022.2123705},
doi={10.1080/02331934.2022.2123705},
url={https://bingtan.me/files/paper/TL-OPT2022.pdf},
abstract={We present two adaptive inertial projection and contraction algorithms to discover the minimum-norm solutions of pseudomonotone variational inequality problems in real Hilbert spaces. The suggested algorithms employ two different step sizes in each iteration and use a non-monotone step size criterion without any line search allowing them to work adaptively. The strong convergence of the iterative sequences formed by the proposed algorithms is established under some mild conditions. Several numerical experiments occurring in finite- and infinite-dimensional Hilbert spaces and applications to optimal control problems as well as signal processing problems are given. Performance profiles are used to verify the computational efficiency and advantages of the proposed algorithms with respect to some known ones.},
keywords={Variational inequality problem,  Inertial method,  Projection and contraction method,  Subgradient extragradient method, Pseudomonotone operator, Optimal control problem, Signal processing problem, Strong convergence},
abbrev_source_title={Optimization},
}



@ARTICLE{TL_ASVAO22,
author={Tan, Bing and Li, Songxiao},
title={Revisiting projection and contraction algorithms for solving variational inequalities and applications},
journal={Applied Set-Valued Analysis and Optimization},
year={2022},
volume={4},
number={2},
pages={167--183},
doi={10.23952/asvao.4.2022.2.03},
url={https://bingtan.me/files/paper/TL-ASVAO2022.pdf},
abstract={We provide two novel projection and contraction algorithms to find the minimum-norm solution of the variational inequality problem with a pseudo monotone and non-Lipschitz continuous operator in a real Hilbert space. Our algorithms can work adaptively without requiring the prior information of the Lipschitz constant of the operator. Strong convergence theorems for the suggested iterative algorithms are established under suitable conditions. Some numerical experiments are discussed to demonstrate the computational efficiency of the proposed algorithms in comparison with several existing ones.},
keywords={Variational inequality problem, Subgradient extragradient method, Projection and contraction method, Inertial method, Pseudomonotone operator},
abbrev_source_title={Appl. Set-Valued Anal. Optim.},
}



@ARTICLE{TZL_JAMC22,
author={Tan, Bing and Zhou, Zheng and Li, Songxiao},
title={Viscosity-type inertial extragradient algorithms for solving variational inequality problems and fixed point problems},
journal={Journal of Applied Mathematics and Computing},
year={2022},
volume={68},
number={2},
pages={1387--1411},
doi={10.1007/s12190-021-01576-z},
url={https://bingtan.me/files/paper/TZL-JAMC2022.pdf},
abstract={The paper presents two inertial viscosity-type extragradient algorithms for finding a common solution of the variational inequality problem involving a monotone and Lipschitz continuous operator and of the fixed point problem with a demicontractive mapping in real Hilbert spaces. Our algorithms use a simple step size rule which is generated by some calculations at each iteration. Two strong convergence theorems are obtained without the prior knowledge of the Lipschitz constant of the operator. The numerical behaviors of the proposed algorithms in some numerical experiments are reported and compared with previously known ones.},
keywords={Fixed point problem,  Inertial method,  Subgradient extragradient method,  Tseng's extragradient method,  Variational inequality problem},
abbrev_source_title={J. Appl. Math. Comput.},
}



@ARTICLE{TLC_JANO22,
author={Tan, Bing and Li, Songxiao and Cho, Sun Y.},
title={Revisiting inertial subgradient extragradient algorithms for solving bilevel variational inequality problems},
journal={Journal of Applied and Numerical Optimization},
year={2022},
volume={4},
number={3},
pages={425--444},
doi={10.23952/jano.4.2022.3.08},
url={https://bingtan.me/files/paper/TLC-JANO2022.pdf},
abstract={In this paper, four modified subgradient extragradient algorithms are proposed for solving bilevel pseudomonotone variational inequality problems in real Hilbert spaces. The proposed algorithms can work adaptively without the prior knowledge of the Lipschitz constant of the pseudomonotone mapping. Strong convergence theorems for the suggested algorithms are established under suitable and mild conditions. Finally, some numerical experiments and applications are performed to verify the efficiency of the proposed algorithms with respect to some previously known ones.},
keywords={Inertial method, Pseudomonotone operator, Subgradient extragradient method, Bilevel variational inequality problem},
abbrev_source_title={J. Appl. Numer. Optim.},
}



@ARTICLE{TCY_JNVA22,
author={Tan, Bing and Cho, Sun Y. and Yao, Jen C.},
title={Accelerated inertial subgradient extragradient algorithms with non-monotonic step sizes for equilibrium problems and fixed point problems},
journal={Journal of Nonlinear and Variational Analysis},
year={2022},
volume={6},
number={1},
pages={89--122},
doi={10.23952/jnva.6.2022.1.06},
url={https://bingtan.me/files/paper/TCY-JNVA2022.pdf},
abstract={This paper introduces several new accelerated subgradient extragradient methods with inertial effects for approximating a solution of a pseudomonotone equilibrium problem and a fixed point problem involving a quasi-nonexpansive mapping or a demicontractive mapping in real Hilbert spaces. The proposed algorithms use an adaptive non-monotonic step size criterion that does not include any Armijo line search process. Strong convergence theorems of the suggested iterative algorithms are established without the prior knowledge of the Lipschitz constants of the bifunction. Moreover, $R$-linear convergence is guaranteed under the assumption that the bifunction satisfies strong pseudomonotonicity. Applications to variational inequality problems are also considered. Finally, some numerical examples and applications, which demonstrate the advantages and efficiency of the proposed algorithms, are given.},
keywords={Equilibrium problem,  Fixed point problem,  Inertial method,  Pseudomonotone bifunction,  Subgradient extragradient method},
abbrev_source_title={J. Nonlinear Var. Anal.},
}



@ARTICLE{TC_CNSNS22,
author={Tan, Bing and Cho, Sun Y.},
title={Two adaptive modified subgradient extragradient methods for bilevel pseudomonotone variational inequalities with applications},
journal={Communications in Nonlinear Science and Numerical Simulation},
year={2022},
volume={107},
doi={10.1016/j.cnsns.2021.106160},
pages={106160},
url={https://bingtan.me/files/paper/TC-CNSNS2022.pdf},
abstract={We consider the bilevel variational inequality problem with a pseudomonotone operator in real Hilbert spaces and investigate two modified subgradient extragradient methods with inertial terms. Our first scheme requires the operator to be Lipschitz continuous (the Lipschitz constant does not need to be known) while the second one only requires it to be uniformly continuous. The proposed methods employ two adaptive stepsizes making them work without the prior knowledge of the Lipschitz constant of the mapping. The strong convergence properties of the iterative sequences generated by the proposed algorithms are obtained under mild conditions. Some numerical tests and applications are given to demonstrate the advantages and efficiency of the stated schemes over previously known ones.},
keywords={Adaptive stepsize,  Bilevel variational inequality problem,  Extragradient method,  Inertial method,  Pseudomonotone operator},
abbrev_source_title={Comm. Nonlinear Sci. Numer. Simul.},
}



@ARTICLE{TC_RCSM22,
author={Tan, Bing and Cho, Sun Y.},
title={Two projection-based methods for bilevel pseudomonotone variational inequalities involving non-Lipschitz operators},
journal={Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas},
year={2022},
volume={116},
number={2},
doi={10.1007/s13398-021-01205-1},
pages={64},
url={https://bingtan.me/files/paper/TC-RACSAM2022.pdf},
abstract={In this paper, we propose two new iterative algorithms to discover solutions of bilevel pseudomonotone variational inequalities with non-Lipschitz continuous operators in real Hilbert spaces. Our proposed algorithms need to compute the projection on the feasible set only once in each iteration although they employ Armijo line search methods. Strong convergence theorems of the suggested algorithms are established under suitable and weaker conditions. Some numerical experiments and applications are given to demonstrate the performance of the offered algorithms compared to some known ones.},
keywords={Armijo stepsize,  Bilevel variational inequality problem,  Inertial method,  Non-Lipschitz operator,  Pseudomonotone operator},
abbrev_source_title={Rev. R. Acad. Cienc. Exactas F{\' i}s. Nat. Ser. A Mat. RACSAM},
}



@ARTICLE{TC_AA22,
author={Tan, Bing and Cho, Sun Y.},
title={Strong convergence of inertial forward-backward methods for solving monotone inclusions},
journal={Applicable Analysis},
year={2022},
volume={101},
number={15},
pages={5386--5414},
doi={10.1080/00036811.2021.1892080},
url={https://bingtan.me/files/paper/TC-AA2022.pdf},
abstract={The paper presents four modifications of the inertial forward–backward splitting method for monotone inclusion problems in the framework of real Hilbert spaces. The advantages of our iterative schemes are that the single-valued operator is Lipschitz continuous monotone rather than cocoercive and the Lipschitz constant does not require to be known. The strong convergence of the suggested approaches is obtained under some standard and mild conditions. Finally, several numerical experiments in finite- and infinite-dimensional spaces are proposed to demonstrate the advantages of our algorithms over the existing related ones.},
keywords={Inclusion problem,  Inertial forward–backward method,  Projection and contraction method,  Tseng's extragradient method,  Viscosity method, Signal processing problem},
abbrev_source_title={Appl. Anal.},
bibbase_note={<span style="color: red">(ESI Highly Cited Paper)</span>},
}



@ARTICLE{TC_COAM22,
author={Tan, Bing and Cho, Sun Y.},
title={Inertial extragradient algorithms with non-monotone stepsizes for pseudomonotone variational inequalities and applications},
journal={Computational and Applied Mathematics},
year={2022},
volume={41},
number={3},
doi={10.1007/s40314-022-01819-0},
pages={121},
url={https://bingtan.me/files/paper/TC-COAM2022.pdf},
abstract={The goal of this paper is to construct several fast iterative algorithms for solving pseudomonotone variational inequalities in real Hilbert spaces. We introduce two extragradient algorithms with inertial terms and give a strong convergence analysis under suitable assumptions. The suggested algorithms need to compute the projection on the feasible set only once in each iteration and can update the step size adaptively without any line search condition. Some numerical experiments and applications are implemented to illustrate the advantages and efficiency of the suggested algorithms over the related known methods.},
keywords={Inertial method,  Pseudomonotone operator,  Subgradient extragradient method,  Tseng's extragradient method,  Variational inequality problem},
abbrev_source_title={Comput. Appl. Math.},
}



@ARTICLE{TC_JNCA22,
author={Tan, Bing and Cho, Sun Y.},
title={Two new projection algorithms for variational inequalities in Hilbert spaces},
journal={Journal of Nonlinear and Convex Analysis},
year={2022},
volume={23},
number={11},
pages={2523--2534},
url={https://bingtan.me/files/paper/TC-JNCA2022.pdf},
abstract={In this paper, two new projection-type algorithms are introduced for solving pseudomonotone variational inequalities in real Hilbert spaces. The proposed methods use two non-monotonic step sizes allowing them to work adaptively without the prior information of the Lipschitz constant of the operator. Strong convergence theorems for the proposed methods are established under suitable conditions. A fundamental numerical example is given to verify the efficiency of the suggested methods in comparison with some known ones.},
keywords={Inertial method, Pseudomonotone operator,  Variational inequality problem, Projection method},
abbrev_source_title={J. Nonlinear Convex Anal.},
}



@ARTICLE{ZTL_MMAS22,
author={Zhou, Zheng and Tan, Bing and Li, Songxiao},
title={Adaptive hybrid steepest descent algorithms involving an inertial extrapolation term for split monotone variational inclusion problems},
journal={Mathematical Methods in the Applied Sciences},
year={2022},
volume={45},
number={15},
pages={8835--8853},
doi={10.1002/mma.7931},
url={https://bingtan.me/files/paper/ZTL-MMAS2022.pdf},
abstract={In this paper, we discuss the split monotone variational inclusion problem and propose two new inertial algorithms in infinite-dimensional Hilbert spaces. The iterative sequence by the proposed algorithms converges strongly to the solution of a certain variational inequality with the help of the hybrid steepest descent method. Furthermore, an adaptive step size criterion is considered in suggested algorithms to avoid the difficulty of calculating the operator norm. Meanwhile, our results are also applied to several other types of split problems. Finally, some numerical experiments show that our algorithms are realistic and summarize the known results.},
keywords={Adaptive stepsize,  Hybrid steepest descent method,  Inertial method,  Signal processing problem,  Strong convergence},
abbrev_source_title={Math. Methods Appl. Sci.},
}



@ARTICLE{ZTC_JNCA22,
author={Zhou, Zheng and Tan, Bing and Cho, Sun Y.},
title={Alternated inertial subgradient extragradient methods for solving variational inequalities},
journal={Journal of Nonlinear and Convex Analysis},
year={2022},
volume={23},
number={11},
pages={2593--2604},
url={https://bingtan.me/files/paper/ZTC-JNCA2022.pdf},
abstract={The goal of this paper is to study some iterative algorithms for solving a pseudomonotone variational inequality in Hilbert spaces. The iterative algorithms presented in this paper are based on the alternated inertial method and the subgradient extragradient method. Weak convergence of the algorithms is established by the adaptive stepsize criterion in Hilbert spaces.},
keywords={Alternated inertial method, Pseudomonotone operator,  Variational inequality problem, Subgradient extragradient method},
abbrev_source_title={J. Nonlinear Convex Anal.},
}



@ARTICLE{ZTL_AIMS22,
author={Zhou, Zheng and Tan, Bing and Li, Songxiao},
title={Two self-adaptive inertial projection algorithms for solving split variational inclusion problems},
journal={AIMS Mathematics},
year={2022},
volume={7},
number={4},
pages={4960--4973},
doi={10.3934/math.2022276},
url={https://bingtan.me/files/paper/ZTL-AIMS2022.pdf},
abstract={This paper is to analyze the approximation solution of a split variational inclusion problem in the framework of Hilbert spaces. For this purpose, inertial hybrid and shrinking projection algorithms are proposed under the effect of a self-adaptive stepsize which does not require information of the norms of the given operators. The strong convergence properties of the proposed algorithms are obtained under mild constraints. Finally, a numerical experiment is given to illustrate the performance of proposed methods and to compare our algorithms with an existing algorithm.},
keywords={Inertial method,  Adaptive stepsize,  Split variational inclusion problem},
abbrev_source_title={AIMS Math.},
}



@ARTICLE{FQT_AA22,
author={Fan, Jingjing and Qin, Xiaolong and Tan, Bing},
title={Tseng's extragradient algorithm for pseudomonotone variational inequalities on {H}adamard manifolds},
journal={Applicable Analysis},
year={2022},
volume={101},
number={6},
pages={2372--2385},
doi={10.1080/00036811.2020.1807012},
url={https://bingtan.me/files/paper/FQT-AA2022.pdf},
abstract={In this paper, we investigate the Tseng's extragradient algorithm for non-Lipschitzian variational inequalities with pseudomonotone vector fields on Hadamard manifolds. The convergence analysis of the proposed algorithm is discussed under mild assumptions. Two experiments are provided to illustrate the asymptotical behavior of the algorithm. The results presented in this paper generalize some known results presented in the literature.},
keywords={Extragradient method,  Hadamard manifolds,  Non-Lipschitz operator,  Pseudomonotone vector field,  Variational inequality problem},
abbrev_source_title={Appl. Anal.},
}



@ARTICLE{TQY_JSC21,
author={Tan, Bing and Qin, Xiaolong and Yao, Jen C.},
title={Strong convergence of self-adaptive inertial algorithms for solving split variational inclusion problems with applications},
journal={Journal of Scientific Computing},
year={2021},
volume={87},
number={1},
doi={10.1007/s10915-021-01428-9},
pages={20},
url={https://bingtan.me/files/paper/TQY-JSC2021.pdf},
abstract={In this paper, four self-adaptive iterative algorithms with inertial effects are introduced to solve a split variational inclusion problem in real Hilbert spaces. One of the advantages of the suggested algorithms is that they can work without knowing the prior information of the operator norm. Strong convergence theorems of these algorithms are established under mild and standard assumptions. As applications, the split feasibility problem and the split minimization problem in real Hilbert spaces are studied. Finally, several preliminary numerical experiments as well as an example in the field of compressed sensing are proposed to support the advantages and efficiency of the suggested methods over some existing ones.},
keywords={Inertial method,  Mann method,  Signal processing problem,  Split variational inclusion problem,  Strong convergence,  Viscosity method},
abbrev_source_title={J. Sci. Comput.},
bibbase_note={<span style="color: red">(ESI Highly Cited Paper)</span>},
}



@ARTICLE{TQY_NUMA21,
author={Tan, Bing and Qin, Xiaolong and Yao, Jen C.},
title={Two modified inertial projection algorithms for bilevel pseudomonotone variational inequalities with applications to optimal control problems},
journal={Numerical Algorithms},
year={2021},
volume={88},
number={4},
pages={1757--1786},
doi={10.1007/s11075-021-01093-x},
url={https://bingtan.me/files/paper/TQY-NUMA2021.pdf},
abstract={In this paper, we investigate two new algorithms for solving bilevel pseudomonotone variational inequality problems in real Hilbert spaces. The advantages of our algorithms are that they only need to calculate one projection on the feasible set in each iteration, and do not require the prior information of the Lipschitz constant of the cost operator. Furthermore, two new algorithms are derived to solve variational inequality problems. We establish the strong convergence of the proposed algorithms under some suitable conditions imposed on parameters. Finally, several numerical results and applications in optimal control problems are reported to illustrate the efficiency and advantages of the proposed algorithms.},
keywords={Bilevel variational inequality problem,  Hybrid steepest descent method,  Inertial extragradient method,  Projection and contraction method,  Pseudomonotone operator},
abbrev_source_title={Numer. Algorithms},
}



@ARTICLE{TLQ_JIAM21,
author={Tan, Bing and Liu, Liya and Qin, Xiaolong},
title={Self adaptive inertial extragradient algorithms for solving bilevel pseudomonotone variational inequality problems},
journal={Japan Journal of Industrial and Applied Mathematics},
year={2021},
volume={38},
number={2},
pages={519-543},
doi={10.1007/s13160-020-00450-y},
url={https://bingtan.me/files/paper/TLQ-JIAM2021.pdf},
abstract={We introduce two inertial extragradient algorithms for solving a bilevel pseudomonotone variational inequality problem in real Hilbert spaces. The advantages of the proposed algorithms are that they can work without the prior knowledge of the Lipschitz constant of the involving operator and only one projection onto the feasible set is required. Strong convergence theorems of the suggested algorithms are obtained under suitable conditions. Finally, some numerical examples are provided to show the efficiency of the proposed algorithms.},
keywords={Bilevel variational inequality problem,  Inertial method, Subgradient extragradient method,  Tseng's extragradient method,  Pseudomonotone operator,  Hybrid steepest descent method},
abbrev_source_title={Jpn J. Ind. Appl. Math.},
bibbase_note={<span style="color: red">(<s>ESI Highly Cited Paper</s>)</span>},
}



@ARTICLE{TFQ_AIOT21,
author={Tan, Bing and Fan, Jingjing and Qin, Xiaolong},
title={Inertial extragradient algorithms with non-monotonic step sizes for solving variational inequalities and fixed point problems},
journal={Advances in Operator Theory},
year={2021},
volume={6},
number={4},
doi={10.1007/s43036-021-00155-0},
pages={61},
url={https://bingtan.me/files/paper/TFQ-AIOT2021.pdf},
abstract={In this paper, we introduce four inertial extragradient algorithms with non-monotonic step sizes to find the solution of the convex feasibility problem, which consists of a monotone variational inequality problem and a fixed point problem with a demicontractive mapping. Strong convergence theorems of the suggested algorithms are established under some standard conditions. Finally, we implement some computational tests to show the efficiency and advantages of the proposed algorithms and compare them with some existing ones.},
keywords={Fixed point problem,  Inertial method,  Strong convergence,  Subgradient extragradient method,  Tseng's extragradient method,  Variational inequality problem},
abbrev_source_title={Adv. Oper. Theory},
}



@ARTICLE{TLQ_ANM21,
author={Tan, Bing and Li, Songxiao and Qin, Xiaolong},
title={Self-adaptive inertial single projection methods for variational inequalities involving non-Lipschitz and Lipschitz operators with their applications to optimal control problems},
journal={Applied Numerical Mathematics},
year={2021},
volume={170},
pages={219--241},
doi={10.1016/j.apnum.2021.07.022},
url={https://bingtan.me/files/paper/TLQ-ANM2021.pdf},
abstract={In this paper, four accelerated subgradient extragradient methods are proposed to solve the variational inequality problem with a pseudo-monotone operator in real Hilbert spaces. These iterative schemes employ two new adaptive stepsize strategies that are significant when the Lipschitz constant of the mapping involved is unknown. Strong convergence theorems for the proposed algorithms are established under the condition that the operators are Lipschitz continuous and non-Lipschitz continuous. Numerical experiments on finite- and infinite-dimensional spaces and applications in optimal control problems are reported to demonstrate the advantages and efficiency of the proposed algorithms over some existing results.},
keywords={Inertial method, Subgradient extragradient method,  Optimal control problem,  Pseudomonotone operator,  Non-Lipschitz operator,  Variational inequality problem},
abbrev_source_title={Appl Numer Math},
}



@ARTICLE{TLQ_RCSM21,
author={Tan, Bing and Li, Songxiao and Qin, Xiaolong},
title={An accelerated extragradient algorithm for bilevel pseudomonotone variational inequality problems with application to optimal control problems},
journal={Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas},
year={2021},
volume={115},
number={4},
doi={10.1007/s13398-021-01116-1},
pages={174},
url={https://bingtan.me/files/paper/TLQ-RACSAM2021.pdf},
abstract={In this paper, an inertial extragradient algorithm with a new non-monotonic stepsize is proposed to solve the bilevel pseudomonotone variational inequality problem in real Hilbert spaces. The advantages of the suggested iterative algorithm are that only one projection onto the feasible set needs to be performed in each iteration and the prior knowledge of the Lipschitz constant of the mapping involved does not require to be known. The strong convergence theorem of the suggested algorithm is established under some suitable conditions. Numerical experiments are reported to illustrate the advantages and efficiency of the presented algorithm over the existing related ones.},
keywords={Bilevel variational inequality problem,  Hybrid steepest descent method,  Inertial extragradient method,  Projection and contraction method,  Pseudomonotone operator},
abbrev_source_title={Rev. R. Acad. Cienc. Exactas F{\' i}s. Nat. Ser. A Mat. RACSAM},
}



@ARTICLE{TLQ_COAM21,
author={Tan, Bing and Li, Songxiao and Qin, Xiaolong},
title={On modified subgradient extragradient methods for pseudomonotone variational inequality problems with applications},
journal={Computational and Applied Mathematics},
year={2021},
volume={40},
number={7},
doi={10.1007/s40314-021-01642-z},
pages={253},
url={https://bingtan.me/files/paper/TLQ-COAM2021.pdf},
abstract={This paper presents several modified subgradient extragradient methods with inertial effects to approximate solutions of variational inequality problems in real Hilbert spaces. The operators involved are either pseudomonotone Lipschitz continuous or pseudomonotone non-Lipschitz continuous. The advantage of the suggested algorithms is that they can work adaptively without the prior information of the Lipschitz constant of the mapping involved. Strong convergence theorems of the proposed algorithms are established under some suitable conditions. Finally, some numerical experiments are given to verify the advantages and efficiency of the proposed iterative algorithms with respect to previously known ones.},
keywords={Extragradient method,  Non-Lipschitz operator,  Optimal control problem,  Pseudomonotone operator,  Variational inequality problem},
abbrev_source_title={Comput. Appl. Math.},
}



@ARTICLE{TFL_COAM21,
author={Tan, Bing and Fan, Jingjing and Li, Songxiao},
title={Self-adaptive inertial extragradient algorithms for solving variational inequality problems},
journal={Computational and Applied Mathematics},
year={2021},
volume={40},
number={1},
doi={10.1007/s40314-020-01393-3},
pages={19},
url={https://bingtan.me/files/paper/TFL-COAM2021.pdf},
abstract={In this paper, we study the strong convergence of two Mann-type inertial extragradient algorithms, which are devised with a new step size, for solving a variational inequality problem with a monotone and Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems for the suggested algorithms are proved without the prior knowledge of the Lipschitz constant of the operator. Finally, we provide some numerical experiments to illustrate the performance of the proposed algorithms and provide a comparison with related ones.},
keywords={Inertial method,  Mann method,  Subgradient extragradient method,  Tseng's extragradient method,  Variational inequality problem},
abbrev_source_title={Comput. Appl. Math.},
bibbase_note={<span style="color: red">(<s>ESI Highly Cited Paper</s>)</span>},
}



@ARTICLE{TC_JNCA21,
author={Tan, Bing and Cho, Sun Y.},
title={Self-adaptive inertial shrinking projection algorithms for solving pseudomonotone variational inequalities},
journal={Journal of Nonlinear and Convex Analysis},
year={2021},
volume={22},
number={3},
pages={613--627},
url={https://bingtan.me/files/paper/TC-JNCA2021.pdf},
abstract={In this paper, we construct two fast iterative methods to solve pseudomonotone variational inequalities in real Hilbert spaces. The advantage of the suggested iterative schemes is that they can adaptively update the iterative step size through some previously known information without performing any line search process. Strong convergence theorems of the proposed algorithms are established under some relaxed conditions imposed on the parameters. Finally, several numerical tests are given to show the advantages and efficiency of the proposed approaches compared with the existing results.},
keywords={Inertial method, Subgradient extragradient method,  Tseng's extragradient method,  Pseudomonotone operator,  Shrinking projection method,  Variational inequality problem},
abbrev_source_title={J. Nonlinear Convex Anal.},
}



@ARTICLE{TC_ASVAO21,
author={Tan, Bing and Cho, Sun Y.},
title={Inertial extragradient methods for solving pseudomonotone variational inequalities with non-lipschitz mappings and their optimization applications},
journal={Applied Set-Valued Analysis and Optimization},
year={2021},
volume={3},
number={2},
pages={165--192},
doi={10.23952/asvao.3.2021.2.03},
url={https://bingtan.me/files/paper/TC-ASVAO2021.pdf},
abstract={In this paper, four extragradient-type algorithms with inertial terms are presented for solving the variational inequality problem with a pseudomonotone and non-Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems of the suggested methods are established under some suitable conditions imposed on the parameters. Finally, several computational tests and applications in optimal control problems are given to illustrate the efficiency and advantages of the proposed iterative schemes over some known ones.},
keywords={Inertial extragradient method,  Non-Lipschitz operator,  Pseudomonotone operator,  Variational inequality problem,  Viscosity method},
abbrev_source_title={Appl. Set-Valued. Anal. Optim.},
}



@ARTICLE{LTL_JNVA21,
author={Liu, Liya and Tan, Bing and Latif, A.},
title={Approximation of fixed points for a semigroup of Bregman quasi-nonexpansive mappings in {B}anach spaces},
journal={Journal of Nonlinear and Variational Analysis},
year={2021},
volume={5},
number={1},
pages={9--22},
doi={10.23952/jnva.5.2021.1.02},
url={https://bingtan.me/files/paper/LTL-JNVA2021.pdf},
abstract={The purpose of this paper is to study the iterative scheme of the Halpern type for a commutative semigroup $\mathfrak{J}=\left\{S_{\lambda}: \lambda \in \mathcal{Q}\right\}$ of Bregman quasi-nonexpansive mappings on a closed and convex subset of a Banach space. A strong convergence theorem is established for finding a common fixed point solution. Our results extend and improve some related results in the current literature. In addition, we present numerical examples to illustrate the performance of our method in finite and infinite dimensional spaces.},
keywords={Banach space,  Bregman quasi-nonexpansive,  Fixed point problem,  Halpern method,  Strong convergence},
abbrev_source_title={J. Nonlinear Var. Anal.},
}



@ARTICLE{ZTL_MMAS21,
author={Zhou, Zheng and Tan, Bing and Li, Songxiao},
title={An accelerated hybrid projection method with a self-adaptive step-size sequence for solving split common fixed point problems},
journal={Mathematical Methods in the Applied Sciences},
year={2021},
volume={44},
number={8},
pages={7294--7303},
doi={10.1002/mma.7261},
url={https://bingtan.me/files/paper/ZTL-MMAS2021.pdf},
abstract={This paper attempts to solve the split common fixed point problem for demicontractive mappings. We give an accelerated hybrid projection algorithm that combines the hybrid projection method and the inertial technique. The strong convergence theorem of this algorithm is obtained under mild conditions by a self-adaptive step-size sequence, which does not need prior knowledge of the operator norm. Some numerical experiments in infinite-dimensional Hilbert spaces are provided to illustrate the reliability and robustness of the algorithm and also to compare it with existing ones.},
keywords={Demicontractive mapping,  Hybrid projection method,  Inertial method,  Split common fixed point problem},
abbrev_source_title={Math. Methods Appl. Sci.},
bibbase_note={<span style="color: red">(<s>ESI Highly Cited Paper</s>)</span>},
}



@ARTICLE{FTL_COAM21,
author={Fan, Jingjing and Tan, Bing and Li, Songxiao},
title={An explicit extragradient algorithm for equilibrium problems on {H}{H}adamard manifolds},
journal={Computational and Applied Mathematics},
year={2021},
volume={40},
number={2},
doi={10.1007/s40314-021-01427-4},
pages={68},
url={https://bingtan.me/files/paper/FTL-COAM2021.pdf},
abstract={In this paper, we investigate a new extragradient algorithm for solving pseudomonotone equilibrium problems on Hadamard manifolds. Our algorithm uses a variable stepsize, which is updated at each iteration and based on some previous iterates. The convergence analysis of the proposed algorithm is discussed under mild assumptions. In the case where the equilibrium bifunction is strongly pseudomonotone, the R-linear rate of convergence of the new algorithm is formulated. A fundamental experiment is provided to illustrate the numerical behavior of the algorithm.},
keywords={Equilibrium problem,  Extragradient method,  Hadamard manifolds,  Lipschitz-type bifunction,  Pseudomonotone bifunction},
abbrev_source_title={Comput. Appl. Math.},
}



@ARTICLE{FQT_NFAO21,
author={Fan, Jingjing and Qin, Xiaolong and Tan, Bing},
title={Convergence of an inertial shadow {D}ouglas-{R}achford splitting algorithm for monotone inclusions},
journal={Numerical Functional Analysis and Optimization},
year={2021},
volume={42},
number={14},
pages={1627--1644},
doi={10.1080/01630563.2021.2001749},
url={https://bingtan.me/files/paper/FQT-NFAO2021.pdf},
abstract={An inertial shadow Douglas-Rachford splitting algorithm for finding zeros of the sum of monotone operators is proposed in Hilbert spaces. Moreover, a three-operator splitting algorithm for solving a class of monotone inclusion problems is also concerned. The weak convergence of the algorithms is investigated under mild assumptions. Some numerical experiments are implemented to illustrate our main convergence results.},
keywords={Inertial method,  Monotone inclusion,  Shadow Douglas-Rachford splitting algorithm,  Three-operator splitting},
abbrev_source_title={Numer. Funct. Anal. Optim.},
}



@ARTICLE{TL_JNVA20,
author={Tan, Bing and Li, Songxiao},
title={Strong convergence of inertial mann algorithms for solving hierarchical fixed point problems},
journal={Journal of Nonlinear and Variational Analysis},
year={2020},
volume={4},
number={3},
pages={337--355},
doi={10.23952/jnva.4.2020.3.02},
url={https://bingtan.me/files/paper/TL-JNVA2020.pdf},
abstract={The paper introduces two inertial Mann algorithms to find solutions of hierarchical fixed point problems of nonexpansive mappings. We obtain strong convergence theorems in Hilbert spaces under suitable conditions. Some numerical examples are provided to illustrate the numerical behavior of the algorithms and numerical results show that our proposed algorithms are efficient and robust.},
keywords={Hierarchical fixed point problem,  Inertial method, Mann method,  Nonexpansive mapping,  Strong convergence,  Viscosity method},
abbrev_source_title={J. Nonlinear Var. Anal.},
}



@ARTICLE{TC_JANO20,
author={Tan, Bing and Cho, Sun Y.},
title={An inertial mann-like algorithm for fixed points of nonexpansive mappings in {H}ilbert spaces},
journal={Journal of Applied and Numerical Optimization},
year={2020},
volume={2},
number={3},
pages={335--351},
doi={10.23952/jano.2.2020.3.05},
url={https://bingtan.me/files/paper/TC-JANO2020.pdf},
abstract={In this paper, we investigate an inertial Mann-like algorithm for fixed points of nonexpansive mappings in Hilbert spaces and obtain strong convergence results under some mild assumptions. Based on this, we derive a forward-backward algorithm involving Tikhonov regularization terms, which converges strongly to the solution of the monotone inclusion problem. We demonstrate the advantages of our algorithms comparing with some existing ones in the literature via split feasibility problem, variational inequality problem and signal recovery problem.},
keywords={Forward-backward splitting algorithm,  Inertial method, Mann method,  Nonexpansive mapping,  Strong convergence,  Tikhonov regularization},
abbrev_source_title={J. Appl. Numer. Optim.},
}



@ARTICLE{TX_JANO20,
author={Tan, Bing and Xu, Shanshan},
title={Strong convergence of two inertial projection algorithms in {H}ilbert spaces},
journal={Journal of Applied and Numerical Optimization},
year={2020},
volume={2},
number={2},
pages={171--186},
doi={10.23952/jano.2.2020.2.04},
url={https://bingtan.me/files/paper/TX-JANO2020.pdf},
abstract={In this paper, we propose two inertial projection algorithms for finding a common solution of monotone variational inclusions and hierarchical fixed point problems of nonexpansive mappings. We obtain two strong convergence theorems under some suitable conditions in Hilbert spaces. In addition, we also give numerical examples to compare our algorithms with the existing ones. Numerical results show that our proposed algorithms are efficient and robust.},
keywords={Hierarchical fixed point problem,  Inertial method,  Monotone operator,  Strong convergence,  Inclusion problem},
abbrev_source_title={J. Appl. Numer. Optim.},
}



@ARTICLE{TZQ_JAAC20,
author={Tan, Bing and Zhou, Zheng and Qin, Xiaolong},
title={Accelerated projection-based forward-backward splitting algorithms for monotone inclusion problems},
journal={Journal of Applied Analysis and Computation},
year={2020},
volume={10},
number={5},
pages={2184--2197},
doi={10.11948/20190363},
url={https://bingtan.me/files/paper/TZQ-JAAC2020.pdf},
abstract={In this paper, based on inertial and Tseng's ideas, we propose two projection-based algorithms to solve a monotone inclusion problem in infinite dimensional Hilbert spaces. Solution theorems of strong convergence are obtained under the certain conditions. Some numerical experiments are presented to illustrate that our algorithms are efficient than the existing results.},
keywords={Forward-backward splitting algorithm,  Inclusion problem,  Monotone operator,  Strong convergence},
abbrev_source_title={J. Appl. Anal. Comput.},
}



@ARTICLE{TXL_JNCA20_2,
author={Tan, Bing and Xu, Shanshan and Li, Songxiao},
title={Inertial shrinking projection algorithms for solving hierarchical variational inequality problems},
journal={Journal of Nonlinear and Convex Analysis},
year={2020},
volume={21},
number={4},
pages={871--884},
url={https://bingtan.me/files/paper/TXL-JNCA2020.pdf},
abstract={In this paper, we propose two inertial shrinking algorithms to approximate a solution of hierarchical variational inequality problems with nonex-pansive mappings in Hilbert spaces. We prove strong convergence theorems under some mild conditions. Finally, we present some numerical examples to compare our algorithms with some existing algorithms, which illustrate the advantage of our proposed algorithms.},
keywords={Hierarchical variational inequality problem,  Inertial method, Mann method,  Nonexpansive mapping,  Shrinking projection method,  Strong convergence},
abbrev_source_title={J. Nonlinear Convex Anal.},
bibbase_note={<span style="color: red">(<s>ESI Highly Cited Paper</s>)</span>},
}



@ARTICLE{TXL_JNCA20_1,
author={Tan, Bing and Xu, Shanshan and Li, Songxiao},
title={Inertial hybrid and shrinking projection algorithms for solving variational inequality problems},
journal={Journal of Nonlinear and Convex Analysis},
year={2020},
volume={21},
number={10},
pages={2193--2206},
url={https://bingtan.me/files/paper/TXL-JNCA2020-10.pdf},
abstract={In this paper, we propose two inertial hybrid and shrinking projection algorithms for strict pseudo-contractions in Hilbert spaces and obtain strong theorems in general conditions. In addition, we also propose two new inertial hybrid and shrinking projection algorithms without extrapolating step for non-expansive mappings in Hilbert spaces and get strong convergence results. Finally, we give some numerical examples to illustrate the computational performance of our proposed algorithms.},
keywords={Variational inequality problem,  Inertial method, Hybrid projection method, Shrinking projection method, Strong convergence},
abbrev_source_title={J. Nonlinear Convex Anal.},
}



@ARTICLE{TXL_MATH20,
author={Tan, Bing and Xu, Shanshan and Li, Songxiao},
title={Modified inertial hybrid and shrinking projection algorithms for solving fixed point problems},
journal={Mathematics},
year={2020},
volume={8},
number={2},
doi={10.3390/math8020236},
pages={236},
url={https://bingtan.me/files/paper/TXL-Math2020.pdf},
abstract={In this paper, we introduce two modified inertial hybrid and shrinking projection algorithms for solving fixed point problems by combining the modified inertial Mann algorithm with the projection algorithm. We establish strong convergence theorems under certain suitable conditions. Finally, our algorithms are applied to convex feasibility problem, variational inequality problem, and location theory. The algorithms and results presented in this paper can summarize and unify corresponding results previously known in this field.},
keywords={Conjugate gradient method,  Hybrid projection method,  Inertial method,  Nonexpansive mapping,  Shrinking projection method,  Hybrid steepest descent method,  Strong convergence},
abbrev_source_title={Mathematics},
}



@ARTICLE{TZL_MATH20,
author={Tan, Bing and Zhou, Zheng and Li, Songxiao},
title={Strong convergence of modified inertial mann algorithms for nonexpansive mappings},
journal={Mathematics},
year={2020},
volume={8},
number={4},
doi={10.3390/math8040462},
pages={462},
url={https://bingtan.me/files/paper/TZL-Math2020.pdf},
abstract={We investigated two new modified inertial Mann Halpern and inertial Mann viscosity algorithms for solving fixed point problems. Strong convergence theorems under some fewer restricted conditions are established in the framework of infinite dimensional Hilbert spaces. Finally, some numerical examples are provided to support our main results. The algorithms and results presented in this paper can generalize and extend corresponding results previously known in the literature.},
keywords={Halpern method,  Inertial method,  Nonexpansive mapping,  Strong convergence,  Viscosity method},
abbrev_source_title={Mathematics},
}



@ARTICLE{LTC_JNCA20,
author={Liu, Liya and Tan, Bing and Cho, Sun Y.},
title={On the resolution of variational inequality problems with a double-hierarchical structure},
journal={Journal of Nonlinear and Convex Analysis},
year={2020},
volume={21},
number={2},
pages={377--386},
url={https://bingtan.me/files/paper/LTC-JNCA2020.pdf},
abstract={In this paper, we discuss a pseudo-monotone variational inequality problem with a variational inequality constraint over a general, nonempty, closed and convex set, which is called the double-hierarchical constrained optimization problem. In addition, we propose an iterative algorithm by incorporating inertial terms in the extragradient algorithm. Strong convergence of the algorithm to the unique solution of the problem is guaranteed under certain assumptions.},
keywords={Constrained optimization problem,  Inertial method, Pseudomonotone operator,  Variational inequality problem},
abbrev_source_title={J. Nonlinear Convex Anal.},
bibbase_note={<span style="color: red">(ESI Highly Cited Paper)</span>},
}



@ARTICLE{ZTL_COAM20,
author={Zhou, Zheng and Tan, Bing and Li, Songxiao},
title={A new accelerated self-adaptive stepsize algorithm with excellent stability for split common fixed point problems},
journal={Computational and Applied Mathematics},
year={2020},
volume={39},
number={3},
doi={10.1007/s40314-020-01237-0},
pages={220},
url={https://bingtan.me/files/paper/ZTL-COAM2020.pdf},
abstract={In the framework of Hilbert spaces, we study the solutions of split common fixed point problems. A new accelerated self-adaptive stepsize algorithm with excellent stability is proposed under the effects of inertial techniques and Meir–Keeler contraction mappings. The strong convergence theorems are obtained without prior knowledge of operator norms. Finally, in applications, our main results in this paper are applied to signal recovery problems.},
keywords={Inertial method,  Meir–Keeler contraction,  Adaptive stepsize,  Signal processing problem, Split common fixed point problem},
abbrev_source_title={Comput. Appl. Math.},
}



@ARTICLE{ZTL_JAAC20,
author={Zhou, Zheng and Tan, Bing and Li, Songxiao},
title={An inertial shrinking projection algorithm for split common fixed point problems},
journal={Journal of Applied Analysis and Computation},
year={2020},
volume={10},
number={5},
pages={2104--2120},
doi={10.11948/20190330},
url={https://bingtan.me/files/paper/ZTL-JAAC2020.pdf},
abstract={In this paper, the purpose is to introduce and study a new modified shrinking projection algorithm with inertial effects, which solves split common fixed point problems in Banach spaces. The corresponding strong convergence theorems are obtained without the assumption of semi-compactness on map-pings. Finally, some numerical examples are presented to illustrate the results in this paper.},
keywords={Inertial method,  Shrinking projection method,  Split common fixed point problem,  Strong convergence},
abbrev_source_title={J. Appl. Anal. Comput.},
}



@ARTICLE{LST_MATH20,
author={Luo, Yinglin and Shang, Meijuan and Tan, Bing},
title={A general inertial viscosity type method for nonexpansive mappings and its applications in signal processing},
journal={Mathematics},
year={2020},
volume={8},
number={2},
doi={10.3390/math8020288},
pages={288},
url={https://bingtan.me/files/paper/LST-Math2020.pdf},
abstract={In this paper, we propose viscosity algorithms with two different inertia parameters for solving fixed points of nonexpansive and strictly pseudocontractive mappings. Strong convergence theorems are obtained in Hilbert spaces and the applications to the signal processing are considered. Moreover, some numerical experiments of proposed algorithms and comparisons with existing algorithms are given to the demonstration of the efficiency of the proposed algorithms. The numerical results show that our algorithms are superior to some related algorithms.},
keywords={Inclusion problem,  Nonexpansive mapping,  Signal processing problem,  Strict pseudo-contraction,  Variational inequality problem},
abbrev_source_title={Mathematics},
}









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Precisely, we prove that the sequence generated by proposed algorithm converges strongly to a common solution of equilibrium problems and fixed point problems. We use an effective self-adaptive step size rule to accelerate the convergence process of our proposed iterative algorithm. Moreover, some numerical results are given to show the effectiveness of the proposed algorithm. The results obtained in this paper extend and improve many recent ones in the literature.},\nkeywords={Inertial method,  Subgradient extragradient method, Equilibrium probelm, Fixed point problem, Strong convergence},\nabbrev_source_title={Optimization},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This paper proposes a new inertial subgradient extragradient method for solving equilibrium problems with pseudomonotone and Lipschitz-type bifunctions and fixed point problems for nonexpansive mappings in real Hilbert spaces. Precisely, we prove that the sequence generated by proposed algorithm converges strongly to a common solution of equilibrium problems and fixed point problems. We use an effective self-adaptive step size rule to accelerate the convergence process of our proposed iterative algorithm. Moreover, some numerical results are given to show the effectiveness of the proposed algorithm. The results obtained in this paper extend and improve many recent ones in the literature.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"zhou-cai-tan-dong-amodifiedgeneralizedversionofprojectedreflectedgradientmethodinhilbertspaces-2023\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Zhou, X.; Cai, G.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Dong, Q. L.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  A modified generalized version of projected reflected gradient method in Hilbert spaces.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Numerical Algorithms</i>, doi:10.1007/s11075-023-01566-1.  2023.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/ZCTD-NUMA2023.pdf\"\n     onclick=\"log_download('zhou-cai-tan-dong-amodifiedgeneralizedversionofprojectedreflectedgradientmethodinhilbertspaces-2023', 'https://bingtan.me/files/paper/ZCTD-NUMA2023.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"A modified generalized version of projected reflected gradient method in Hilbert spaces [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s11075-023-01566-1\"\n     onclick=\"log_download('zhou-cai-tan-dong-amodifiedgeneralizedversionofprojectedreflectedgradientmethodinhilbertspaces-2023', 'http://doi.org/10.1007/s11075-023-01566-1', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/zhou-cai-tan-dong-amodifiedgeneralizedversionofprojectedreflectedgradientmethodinhilbertspaces-2023\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('zhou-cai-tan-dong-amodifiedgeneralizedversionofprojectedreflectedgradientmethodinhilbertspaces-2023')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{ZCTD_NUMA23,\nauthor={Zhou, Xiaolin and Cai, Gang and Tan, Bing and Dong, Qiao L.},\ntitle={A modified generalized version of projected reflected gradient method in Hilbert spaces},\njournal={Numerical Algorithms},\nyear={2023},\nvolume={doi:10.1007/s11075-023-01566-1},\ndoi={10.1007/s11075-023-01566-1},\nurl={https://bingtan.me/files/paper/ZCTD-NUMA2023.pdf},\nabstract={This article is concerned with a universal version of projected reflected gradient method with new step size for solving variational inequality problem in Hilbert spaces. Under appropriate assumptions controlled by the operators and parameters, we acquire the weak convergence of the proposed algorithm. We establish an R-linear convergence rate of our method on the condition that the relevant mapping is strongly monotone. We rework our first algorithm so that it can be simplified to several generalized methods in the literature. The efficacy and availability of our proposed iterative scheme are demonstrated in numerical experiments.},\nkeywords={Projected reflected gradient method, Variational inequality, Weak and linear convergence, Hilbert spaces},\nabbrev_source_title={Numer. Algorithms},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This article is concerned with a universal version of projected reflected gradient method with new step size for solving variational inequality problem in Hilbert spaces. Under appropriate assumptions controlled by the operators and parameters, we acquire the weak convergence of the proposed algorithm. We establish an R-linear convergence rate of our method on the condition that the relevant mapping is strongly monotone. We rework our first algorithm so that it can be simplified to several generalized methods in the literature. The efficacy and availability of our proposed iterative scheme are demonstrated in numerical experiments.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_Cho__S_\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_Cho__S_')\"\n      onkeypress=\"toggleGroup('group_Cho__S_')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>Cho, S.</span>\n      <span class=\"bibbase_group_count\">\n        \n        (14)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"tan-li-cho-inertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalitieswithnonlipschitzoperatorsandapplications-2023\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Li, S.;  and Cho, S. Y.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Inertial projection and contraction methods for pseudomonotone variational inequalities with non-Lipschitz operators and applications.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Applicable Analysis</i>, 102(4): 1199–1221.  2023.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TLC-AA2023.pdf\"\n     onclick=\"log_download('tan-li-cho-inertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalitieswithnonlipschitzoperatorsandapplications-2023', 'https://bingtan.me/files/paper/TLC-AA2023.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Inertial projection and contraction methods for pseudomonotone variational inequalities with non-Lipschitz operators and applications [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1080/00036811.2021.1979219\"\n     onclick=\"log_download('tan-li-cho-inertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalitieswithnonlipschitzoperatorsandapplications-2023', 'http://doi.org/10.1080/00036811.2021.1979219', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-li-cho-inertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalitieswithnonlipschitzoperatorsandapplications-2023\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-li-cho-inertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalitieswithnonlipschitzoperatorsandapplications-2023')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TLC_AA23,\nauthor={Tan, Bing and Li, Songxiao and Cho, Sun Y.},\ntitle={Inertial projection and contraction methods for pseudomonotone variational inequalities with non-Lipschitz operators and applications},\njournal={Applicable Analysis},\nyear={2023},\nvolume={102},\nnumber={4},\ndoi={10.1080/00036811.2021.1979219},\npages={1199--1221},\nurl={https://bingtan.me/files/paper/TLC-AA2023.pdf},\nabstract={In this paper, some new accelerated iterative schemes are proposed to solve the variational inequality problem with a pseudomonotone and uniformly continuous operator in real Hilbert spaces. Strong convergence theorems of the suggested algorithms are obtained without the prior knowledge of the Lipschitz constant of the operator. Some numerical experiments and applications are performed to illustrate the advantages of the proposed methods with respect to several related ones.},\nkeywords={Inertial extragradient method,  Projection and contraction method,  Pseudomonotone operator,  Non-Lipschitz operator,  Variational inequality problem},\nabbrev_source_title={Appl. Anal.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, some new accelerated iterative schemes are proposed to solve the variational inequality problem with a pseudomonotone and uniformly continuous operator in real Hilbert spaces. Strong convergence theorems of the suggested algorithms are obtained without the prior knowledge of the Lipschitz constant of the operator. Some numerical experiments and applications are performed to illustrate the advantages of the proposed methods with respect to several related ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-qin-cho-revisitingsubgradientextragradientmethodsforsolvingvariationalinequalities-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Qin, X.;  and Cho, S. Y.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Revisiting subgradient extragradient methods for solving variational inequalities.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Numerical Algorithms</i>, 90(4): 1593–1615.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TQC-NUMA2022.pdf\"\n     onclick=\"log_download('tan-qin-cho-revisitingsubgradientextragradientmethodsforsolvingvariationalinequalities-2022', 'https://bingtan.me/files/paper/TQC-NUMA2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Revisiting subgradient extragradient methods for solving variational inequalities [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s11075-021-01243-1\"\n     onclick=\"log_download('tan-qin-cho-revisitingsubgradientextragradientmethodsforsolvingvariationalinequalities-2022', 'http://doi.org/10.1007/s11075-021-01243-1', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-qin-cho-revisitingsubgradientextragradientmethodsforsolvingvariationalinequalities-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>2 downloads</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-qin-cho-revisitingsubgradientextragradientmethodsforsolvingvariationalinequalities-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TQC_NUMA22,\nauthor={Tan, Bing and Qin, Xiaolong and Cho, Sun Y.},\ntitle={Revisiting subgradient extragradient methods for solving variational inequalities},\njournal={Numerical Algorithms},\nyear={2022},\nvolume={90},\nnumber={4},\npages={1593--1615},\ndoi={10.1007/s11075-021-01243-1},\nurl={https://bingtan.me/files/paper/TQC-NUMA2022.pdf},\nabstract={In this paper, several extragradient algorithms with inertial effects and adaptive non-monotonic step sizes are proposed to solve pseudomonotone variational inequalities in real Hilbert spaces. The strong convergence of the proposed methods is established without the prior knowledge of the Lipschitz constant of the mapping. Some numerical experiments are given to illustrate the advantages and efficiency of the proposed schemes over previously known ones.},\nkeywords={Armijo stepsize,  Inertial extragradient method,  Non-Lipschitz operator,  Pseudomonotone operator,  Variational inequality problem},\nabbrev_source_title={Numer. Algorithms},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, several extragradient algorithms with inertial effects and adaptive non-monotonic step sizes are proposed to solve pseudomonotone variational inequalities in real Hilbert spaces. The strong convergence of the proposed methods is established without the prior knowledge of the Lipschitz constant of the mapping. Some numerical experiments are given to illustrate the advantages and efficiency of the proposed schemes over previously known ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-li-cho-revisitinginertialsubgradientextragradientalgorithmsforsolvingbilevelvariationalinequalityproblems-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Li, S.;  and Cho, S. Y.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Revisiting inertial subgradient extragradient algorithms for solving bilevel variational inequality problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Applied and Numerical Optimization</i>, 4(3): 425–444.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TLC-JANO2022.pdf\"\n     onclick=\"log_download('tan-li-cho-revisitinginertialsubgradientextragradientalgorithmsforsolvingbilevelvariationalinequalityproblems-2022', 'https://bingtan.me/files/paper/TLC-JANO2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Revisiting inertial subgradient extragradient algorithms for solving bilevel variational inequality problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.23952/jano.4.2022.3.08\"\n     onclick=\"log_download('tan-li-cho-revisitinginertialsubgradientextragradientalgorithmsforsolvingbilevelvariationalinequalityproblems-2022', 'http://doi.org/10.23952/jano.4.2022.3.08', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-li-cho-revisitinginertialsubgradientextragradientalgorithmsforsolvingbilevelvariationalinequalityproblems-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>1 download</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-li-cho-revisitinginertialsubgradientextragradientalgorithmsforsolvingbilevelvariationalinequalityproblems-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TLC_JANO22,\nauthor={Tan, Bing and Li, Songxiao and Cho, Sun Y.},\ntitle={Revisiting inertial subgradient extragradient algorithms for solving bilevel variational inequality problems},\njournal={Journal of Applied and Numerical Optimization},\nyear={2022},\nvolume={4},\nnumber={3},\npages={425--444},\ndoi={10.23952/jano.4.2022.3.08},\nurl={https://bingtan.me/files/paper/TLC-JANO2022.pdf},\nabstract={In this paper, four modified subgradient extragradient algorithms are proposed for solving bilevel pseudomonotone variational inequality problems in real Hilbert spaces. The proposed algorithms can work adaptively without the prior knowledge of the Lipschitz constant of the pseudomonotone mapping. Strong convergence theorems for the suggested algorithms are established under suitable and mild conditions. Finally, some numerical experiments and applications are performed to verify the efficiency of the proposed algorithms with respect to some previously known ones.},\nkeywords={Inertial method, Pseudomonotone operator, Subgradient extragradient method, Bilevel variational inequality problem},\nabbrev_source_title={J. Appl. Numer. Optim.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, four modified subgradient extragradient algorithms are proposed for solving bilevel pseudomonotone variational inequality problems in real Hilbert spaces. The proposed algorithms can work adaptively without the prior knowledge of the Lipschitz constant of the pseudomonotone mapping. Strong convergence theorems for the suggested algorithms are established under suitable and mild conditions. Finally, some numerical experiments and applications are performed to verify the efficiency of the proposed algorithms with respect to some previously known ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-cho-yao-acceleratedinertialsubgradientextragradientalgorithmswithnonmonotonicstepsizesforequilibriumproblemsandfixedpointproblems-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Cho, S. Y.;  and Yao, J. C.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Accelerated inertial subgradient extragradient algorithms with non-monotonic step sizes for equilibrium problems and fixed point problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Nonlinear and Variational Analysis</i>, 6(1): 89–122.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TCY-JNVA2022.pdf\"\n     onclick=\"log_download('tan-cho-yao-acceleratedinertialsubgradientextragradientalgorithmswithnonmonotonicstepsizesforequilibriumproblemsandfixedpointproblems-2022', 'https://bingtan.me/files/paper/TCY-JNVA2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Accelerated inertial subgradient extragradient algorithms with non-monotonic step sizes for equilibrium problems and fixed point problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.23952/jnva.6.2022.1.06\"\n     onclick=\"log_download('tan-cho-yao-acceleratedinertialsubgradientextragradientalgorithmswithnonmonotonicstepsizesforequilibriumproblemsandfixedpointproblems-2022', 'http://doi.org/10.23952/jnva.6.2022.1.06', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-cho-yao-acceleratedinertialsubgradientextragradientalgorithmswithnonmonotonicstepsizesforequilibriumproblemsandfixedpointproblems-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-cho-yao-acceleratedinertialsubgradientextragradientalgorithmswithnonmonotonicstepsizesforequilibriumproblemsandfixedpointproblems-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TCY_JNVA22,\nauthor={Tan, Bing and Cho, Sun Y. and Yao, Jen C.},\ntitle={Accelerated inertial subgradient extragradient algorithms with non-monotonic step sizes for equilibrium problems and fixed point problems},\njournal={Journal of Nonlinear and Variational Analysis},\nyear={2022},\nvolume={6},\nnumber={1},\npages={89--122},\ndoi={10.23952/jnva.6.2022.1.06},\nurl={https://bingtan.me/files/paper/TCY-JNVA2022.pdf},\nabstract={This paper introduces several new accelerated subgradient extragradient methods with inertial effects for approximating a solution of a pseudomonotone equilibrium problem and a fixed point problem involving a quasi-nonexpansive mapping or a demicontractive mapping in real Hilbert spaces. The proposed algorithms use an adaptive non-monotonic step size criterion that does not include any Armijo line search process. Strong convergence theorems of the suggested iterative algorithms are established without the prior knowledge of the Lipschitz constants of the bifunction. Moreover, $R$-linear convergence is guaranteed under the assumption that the bifunction satisfies strong pseudomonotonicity. Applications to variational inequality problems are also considered. Finally, some numerical examples and applications, which demonstrate the advantages and efficiency of the proposed algorithms, are given.},\nkeywords={Equilibrium problem,  Fixed point problem,  Inertial method,  Pseudomonotone bifunction,  Subgradient extragradient method},\nabbrev_source_title={J. Nonlinear Var. Anal.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This paper introduces several new accelerated subgradient extragradient methods with inertial effects for approximating a solution of a pseudomonotone equilibrium problem and a fixed point problem involving a quasi-nonexpansive mapping or a demicontractive mapping in real Hilbert spaces. The proposed algorithms use an adaptive non-monotonic step size criterion that does not include any Armijo line search process. Strong convergence theorems of the suggested iterative algorithms are established without the prior knowledge of the Lipschitz constants of the bifunction. Moreover, $R$-linear convergence is guaranteed under the assumption that the bifunction satisfies strong pseudomonotonicity. Applications to variational inequality problems are also considered. Finally, some numerical examples and applications, which demonstrate the advantages and efficiency of the proposed algorithms, are given.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-cho-twoadaptivemodifiedsubgradientextragradientmethodsforbilevelpseudomonotonevariationalinequalitieswithapplications-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Cho, S. Y.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Two adaptive modified subgradient extragradient methods for bilevel pseudomonotone variational inequalities with applications.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Communications in Nonlinear Science and Numerical Simulation</i>, 107: 106160.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TC-CNSNS2022.pdf\"\n     onclick=\"log_download('tan-cho-twoadaptivemodifiedsubgradientextragradientmethodsforbilevelpseudomonotonevariationalinequalitieswithapplications-2022', 'https://bingtan.me/files/paper/TC-CNSNS2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Two adaptive modified subgradient extragradient methods for bilevel pseudomonotone variational inequalities with applications [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1016/j.cnsns.2021.106160\"\n     onclick=\"log_download('tan-cho-twoadaptivemodifiedsubgradientextragradientmethodsforbilevelpseudomonotonevariationalinequalitieswithapplications-2022', 'http://doi.org/10.1016/j.cnsns.2021.106160', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-cho-twoadaptivemodifiedsubgradientextragradientmethodsforbilevelpseudomonotonevariationalinequalitieswithapplications-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-cho-twoadaptivemodifiedsubgradientextragradientmethodsforbilevelpseudomonotonevariationalinequalitieswithapplications-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TC_CNSNS22,\nauthor={Tan, Bing and Cho, Sun Y.},\ntitle={Two adaptive modified subgradient extragradient methods for bilevel pseudomonotone variational inequalities with applications},\njournal={Communications in Nonlinear Science and Numerical Simulation},\nyear={2022},\nvolume={107},\ndoi={10.1016/j.cnsns.2021.106160},\npages={106160},\nurl={https://bingtan.me/files/paper/TC-CNSNS2022.pdf},\nabstract={We consider the bilevel variational inequality problem with a pseudomonotone operator in real Hilbert spaces and investigate two modified subgradient extragradient methods with inertial terms. Our first scheme requires the operator to be Lipschitz continuous (the Lipschitz constant does not need to be known) while the second one only requires it to be uniformly continuous. The proposed methods employ two adaptive stepsizes making them work without the prior knowledge of the Lipschitz constant of the mapping. The strong convergence properties of the iterative sequences generated by the proposed algorithms are obtained under mild conditions. Some numerical tests and applications are given to demonstrate the advantages and efficiency of the stated schemes over previously known ones.},\nkeywords={Adaptive stepsize,  Bilevel variational inequality problem,  Extragradient method,  Inertial method,  Pseudomonotone operator},\nabbrev_source_title={Comm. Nonlinear Sci. Numer. Simul.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We consider the bilevel variational inequality problem with a pseudomonotone operator in real Hilbert spaces and investigate two modified subgradient extragradient methods with inertial terms. Our first scheme requires the operator to be Lipschitz continuous (the Lipschitz constant does not need to be known) while the second one only requires it to be uniformly continuous. The proposed methods employ two adaptive stepsizes making them work without the prior knowledge of the Lipschitz constant of the mapping. The strong convergence properties of the iterative sequences generated by the proposed algorithms are obtained under mild conditions. Some numerical tests and applications are given to demonstrate the advantages and efficiency of the stated schemes over previously known ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-cho-twoprojectionbasedmethodsforbilevelpseudomonotonevariationalinequalitiesinvolvingnonlipschitzoperators-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Cho, S. Y.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Two projection-based methods for bilevel pseudomonotone variational inequalities involving non-Lipschitz operators.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas</i>, 116(2): 64.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TC-RACSAM2022.pdf\"\n     onclick=\"log_download('tan-cho-twoprojectionbasedmethodsforbilevelpseudomonotonevariationalinequalitiesinvolvingnonlipschitzoperators-2022', 'https://bingtan.me/files/paper/TC-RACSAM2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Two projection-based methods for bilevel pseudomonotone variational inequalities involving non-Lipschitz operators [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s13398-021-01205-1\"\n     onclick=\"log_download('tan-cho-twoprojectionbasedmethodsforbilevelpseudomonotonevariationalinequalitiesinvolvingnonlipschitzoperators-2022', 'http://doi.org/10.1007/s13398-021-01205-1', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-cho-twoprojectionbasedmethodsforbilevelpseudomonotonevariationalinequalitiesinvolvingnonlipschitzoperators-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-cho-twoprojectionbasedmethodsforbilevelpseudomonotonevariationalinequalitiesinvolvingnonlipschitzoperators-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TC_RCSM22,\nauthor={Tan, Bing and Cho, Sun Y.},\ntitle={Two projection-based methods for bilevel pseudomonotone variational inequalities involving non-Lipschitz operators},\njournal={Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas},\nyear={2022},\nvolume={116},\nnumber={2},\ndoi={10.1007/s13398-021-01205-1},\npages={64},\nurl={https://bingtan.me/files/paper/TC-RACSAM2022.pdf},\nabstract={In this paper, we propose two new iterative algorithms to discover solutions of bilevel pseudomonotone variational inequalities with non-Lipschitz continuous operators in real Hilbert spaces. Our proposed algorithms need to compute the projection on the feasible set only once in each iteration although they employ Armijo line search methods. Strong convergence theorems of the suggested algorithms are established under suitable and weaker conditions. Some numerical experiments and applications are given to demonstrate the performance of the offered algorithms compared to some known ones.},\nkeywords={Armijo stepsize,  Bilevel variational inequality problem,  Inertial method,  Non-Lipschitz operator,  Pseudomonotone operator},\nabbrev_source_title={Rev. R. Acad. Cienc. Exactas F{\\&#x27; i}s. Nat. Ser. A Mat. RACSAM},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we propose two new iterative algorithms to discover solutions of bilevel pseudomonotone variational inequalities with non-Lipschitz continuous operators in real Hilbert spaces. Our proposed algorithms need to compute the projection on the feasible set only once in each iteration although they employ Armijo line search methods. Strong convergence theorems of the suggested algorithms are established under suitable and weaker conditions. Some numerical experiments and applications are given to demonstrate the performance of the offered algorithms compared to some known ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-cho-strongconvergenceofinertialforwardbackwardmethodsforsolvingmonotoneinclusions-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Cho, S. Y.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Strong convergence of inertial forward-backward methods for solving monotone inclusions.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Applicable Analysis</i>, 101(15): 5386–5414.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><span style=\"color: red\">(ESI Highly Cited Paper)</span></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TC-AA2022.pdf\"\n     onclick=\"log_download('tan-cho-strongconvergenceofinertialforwardbackwardmethodsforsolvingmonotoneinclusions-2022', 'https://bingtan.me/files/paper/TC-AA2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Strong convergence of inertial forward-backward methods for solving monotone inclusions [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1080/00036811.2021.1892080\"\n     onclick=\"log_download('tan-cho-strongconvergenceofinertialforwardbackwardmethodsforsolvingmonotoneinclusions-2022', 'http://doi.org/10.1080/00036811.2021.1892080', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-cho-strongconvergenceofinertialforwardbackwardmethodsforsolvingmonotoneinclusions-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-cho-strongconvergenceofinertialforwardbackwardmethodsforsolvingmonotoneinclusions-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TC_AA22,\nauthor={Tan, Bing and Cho, Sun Y.},\ntitle={Strong convergence of inertial forward-backward methods for solving monotone inclusions},\njournal={Applicable Analysis},\nyear={2022},\nvolume={101},\nnumber={15},\npages={5386--5414},\ndoi={10.1080/00036811.2021.1892080},\nurl={https://bingtan.me/files/paper/TC-AA2022.pdf},\nabstract={The paper presents four modifications of the inertial forward–backward splitting method for monotone inclusion problems in the framework of real Hilbert spaces. The advantages of our iterative schemes are that the single-valued operator is Lipschitz continuous monotone rather than cocoercive and the Lipschitz constant does not require to be known. The strong convergence of the suggested approaches is obtained under some standard and mild conditions. Finally, several numerical experiments in finite- and infinite-dimensional spaces are proposed to demonstrate the advantages of our algorithms over the existing related ones.},\nkeywords={Inclusion problem,  Inertial forward–backward method,  Projection and contraction method,  Tseng&#x27;s extragradient method,  Viscosity method, Signal processing problem},\nabbrev_source_title={Appl. Anal.},\nbibbase_note={&lt;span style=&quot;color: red&quot;&gt;(ESI Highly Cited Paper)&lt;/span&gt;},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  The paper presents four modifications of the inertial forward–backward splitting method for monotone inclusion problems in the framework of real Hilbert spaces. The advantages of our iterative schemes are that the single-valued operator is Lipschitz continuous monotone rather than cocoercive and the Lipschitz constant does not require to be known. The strong convergence of the suggested approaches is obtained under some standard and mild conditions. Finally, several numerical experiments in finite- and infinite-dimensional spaces are proposed to demonstrate the advantages of our algorithms over the existing related ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-cho-inertialextragradientalgorithmswithnonmonotonestepsizesforpseudomonotonevariationalinequalitiesandapplications-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Cho, S. Y.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Inertial extragradient algorithms with non-monotone stepsizes for pseudomonotone variational inequalities and applications.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Computational and Applied Mathematics</i>, 41(3): 121.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TC-COAM2022.pdf\"\n     onclick=\"log_download('tan-cho-inertialextragradientalgorithmswithnonmonotonestepsizesforpseudomonotonevariationalinequalitiesandapplications-2022', 'https://bingtan.me/files/paper/TC-COAM2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Inertial extragradient algorithms with non-monotone stepsizes for pseudomonotone variational inequalities and applications [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s40314-022-01819-0\"\n     onclick=\"log_download('tan-cho-inertialextragradientalgorithmswithnonmonotonestepsizesforpseudomonotonevariationalinequalitiesandapplications-2022', 'http://doi.org/10.1007/s40314-022-01819-0', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-cho-inertialextragradientalgorithmswithnonmonotonestepsizesforpseudomonotonevariationalinequalitiesandapplications-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-cho-inertialextragradientalgorithmswithnonmonotonestepsizesforpseudomonotonevariationalinequalitiesandapplications-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TC_COAM22,\nauthor={Tan, Bing and Cho, Sun Y.},\ntitle={Inertial extragradient algorithms with non-monotone stepsizes for pseudomonotone variational inequalities and applications},\njournal={Computational and Applied Mathematics},\nyear={2022},\nvolume={41},\nnumber={3},\ndoi={10.1007/s40314-022-01819-0},\npages={121},\nurl={https://bingtan.me/files/paper/TC-COAM2022.pdf},\nabstract={The goal of this paper is to construct several fast iterative algorithms for solving pseudomonotone variational inequalities in real Hilbert spaces. We introduce two extragradient algorithms with inertial terms and give a strong convergence analysis under suitable assumptions. The suggested algorithms need to compute the projection on the feasible set only once in each iteration and can update the step size adaptively without any line search condition. Some numerical experiments and applications are implemented to illustrate the advantages and efficiency of the suggested algorithms over the related known methods.},\nkeywords={Inertial method,  Pseudomonotone operator,  Subgradient extragradient method,  Tseng&#x27;s extragradient method,  Variational inequality problem},\nabbrev_source_title={Comput. Appl. Math.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  The goal of this paper is to construct several fast iterative algorithms for solving pseudomonotone variational inequalities in real Hilbert spaces. We introduce two extragradient algorithms with inertial terms and give a strong convergence analysis under suitable assumptions. The suggested algorithms need to compute the projection on the feasible set only once in each iteration and can update the step size adaptively without any line search condition. Some numerical experiments and applications are implemented to illustrate the advantages and efficiency of the suggested algorithms over the related known methods.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-cho-twonewprojectionalgorithmsforvariationalinequalitiesinhilbertspaces-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Cho, S. Y.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Two new projection algorithms for variational inequalities in Hilbert spaces.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Nonlinear and Convex Analysis</i>, 23(11): 2523–2534.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TC-JNCA2022.pdf\"\n     onclick=\"log_download('tan-cho-twonewprojectionalgorithmsforvariationalinequalitiesinhilbertspaces-2022', 'https://bingtan.me/files/paper/TC-JNCA2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Two new projection algorithms for variational inequalities in Hilbert spaces [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-cho-twonewprojectionalgorithmsforvariationalinequalitiesinhilbertspaces-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-cho-twonewprojectionalgorithmsforvariationalinequalitiesinhilbertspaces-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TC_JNCA22,\nauthor={Tan, Bing and Cho, Sun Y.},\ntitle={Two new projection algorithms for variational inequalities in Hilbert spaces},\njournal={Journal of Nonlinear and Convex Analysis},\nyear={2022},\nvolume={23},\nnumber={11},\npages={2523--2534},\nurl={https://bingtan.me/files/paper/TC-JNCA2022.pdf},\nabstract={In this paper, two new projection-type algorithms are introduced for solving pseudomonotone variational inequalities in real Hilbert spaces. The proposed methods use two non-monotonic step sizes allowing them to work adaptively without the prior information of the Lipschitz constant of the operator. Strong convergence theorems for the proposed methods are established under suitable conditions. A fundamental numerical example is given to verify the efficiency of the suggested methods in comparison with some known ones.},\nkeywords={Inertial method, Pseudomonotone operator,  Variational inequality problem, Projection method},\nabbrev_source_title={J. Nonlinear Convex Anal.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, two new projection-type algorithms are introduced for solving pseudomonotone variational inequalities in real Hilbert spaces. The proposed methods use two non-monotonic step sizes allowing them to work adaptively without the prior information of the Lipschitz constant of the operator. Strong convergence theorems for the proposed methods are established under suitable conditions. A fundamental numerical example is given to verify the efficiency of the suggested methods in comparison with some known ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"zhou-tan-cho-alternatedinertialsubgradientextragradientmethodsforsolvingvariationalinequalities-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Zhou, Z.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Cho, S. Y.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Alternated inertial subgradient extragradient methods for solving variational inequalities.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Nonlinear and Convex Analysis</i>, 23(11): 2593–2604.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/ZTC-JNCA2022.pdf\"\n     onclick=\"log_download('zhou-tan-cho-alternatedinertialsubgradientextragradientmethodsforsolvingvariationalinequalities-2022', 'https://bingtan.me/files/paper/ZTC-JNCA2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Alternated inertial subgradient extragradient methods for solving variational inequalities [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/zhou-tan-cho-alternatedinertialsubgradientextragradientmethodsforsolvingvariationalinequalities-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('zhou-tan-cho-alternatedinertialsubgradientextragradientmethodsforsolvingvariationalinequalities-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{ZTC_JNCA22,\nauthor={Zhou, Zheng and Tan, Bing and Cho, Sun Y.},\ntitle={Alternated inertial subgradient extragradient methods for solving variational inequalities},\njournal={Journal of Nonlinear and Convex Analysis},\nyear={2022},\nvolume={23},\nnumber={11},\npages={2593--2604},\nurl={https://bingtan.me/files/paper/ZTC-JNCA2022.pdf},\nabstract={The goal of this paper is to study some iterative algorithms for solving a pseudomonotone variational inequality in Hilbert spaces. The iterative algorithms presented in this paper are based on the alternated inertial method and the subgradient extragradient method. Weak convergence of the algorithms is established by the adaptive stepsize criterion in Hilbert spaces.},\nkeywords={Alternated inertial method, Pseudomonotone operator,  Variational inequality problem, Subgradient extragradient method},\nabbrev_source_title={J. Nonlinear Convex Anal.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  The goal of this paper is to study some iterative algorithms for solving a pseudomonotone variational inequality in Hilbert spaces. The iterative algorithms presented in this paper are based on the alternated inertial method and the subgradient extragradient method. Weak convergence of the algorithms is established by the adaptive stepsize criterion in Hilbert spaces.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-cho-selfadaptiveinertialshrinkingprojectionalgorithmsforsolvingpseudomonotonevariationalinequalities-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Cho, S. Y.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Self-adaptive inertial shrinking projection algorithms for solving pseudomonotone variational inequalities.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Nonlinear and Convex Analysis</i>, 22(3): 613–627.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TC-JNCA2021.pdf\"\n     onclick=\"log_download('tan-cho-selfadaptiveinertialshrinkingprojectionalgorithmsforsolvingpseudomonotonevariationalinequalities-2021', 'https://bingtan.me/files/paper/TC-JNCA2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Self-adaptive inertial shrinking projection algorithms for solving pseudomonotone variational inequalities [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-cho-selfadaptiveinertialshrinkingprojectionalgorithmsforsolvingpseudomonotonevariationalinequalities-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-cho-selfadaptiveinertialshrinkingprojectionalgorithmsforsolvingpseudomonotonevariationalinequalities-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TC_JNCA21,\nauthor={Tan, Bing and Cho, Sun Y.},\ntitle={Self-adaptive inertial shrinking projection algorithms for solving pseudomonotone variational inequalities},\njournal={Journal of Nonlinear and Convex Analysis},\nyear={2021},\nvolume={22},\nnumber={3},\npages={613--627},\nurl={https://bingtan.me/files/paper/TC-JNCA2021.pdf},\nabstract={In this paper, we construct two fast iterative methods to solve pseudomonotone variational inequalities in real Hilbert spaces. The advantage of the suggested iterative schemes is that they can adaptively update the iterative step size through some previously known information without performing any line search process. Strong convergence theorems of the proposed algorithms are established under some relaxed conditions imposed on the parameters. Finally, several numerical tests are given to show the advantages and efficiency of the proposed approaches compared with the existing results.},\nkeywords={Inertial method, Subgradient extragradient method,  Tseng&#x27;s extragradient method,  Pseudomonotone operator,  Shrinking projection method,  Variational inequality problem},\nabbrev_source_title={J. Nonlinear Convex Anal.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we construct two fast iterative methods to solve pseudomonotone variational inequalities in real Hilbert spaces. The advantage of the suggested iterative schemes is that they can adaptively update the iterative step size through some previously known information without performing any line search process. Strong convergence theorems of the proposed algorithms are established under some relaxed conditions imposed on the parameters. Finally, several numerical tests are given to show the advantages and efficiency of the proposed approaches compared with the existing results.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-cho-inertialextragradientmethodsforsolvingpseudomonotonevariationalinequalitieswithnonlipschitzmappingsandtheiroptimizationapplications-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Cho, S. Y.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Inertial extragradient methods for solving pseudomonotone variational inequalities with non-lipschitz mappings and their optimization applications.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Applied Set-Valued Analysis and Optimization</i>, 3(2): 165–192.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TC-ASVAO2021.pdf\"\n     onclick=\"log_download('tan-cho-inertialextragradientmethodsforsolvingpseudomonotonevariationalinequalitieswithnonlipschitzmappingsandtheiroptimizationapplications-2021', 'https://bingtan.me/files/paper/TC-ASVAO2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Inertial extragradient methods for solving pseudomonotone variational inequalities with non-lipschitz mappings and their optimization applications [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.23952/asvao.3.2021.2.03\"\n     onclick=\"log_download('tan-cho-inertialextragradientmethodsforsolvingpseudomonotonevariationalinequalitieswithnonlipschitzmappingsandtheiroptimizationapplications-2021', 'http://doi.org/10.23952/asvao.3.2021.2.03', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-cho-inertialextragradientmethodsforsolvingpseudomonotonevariationalinequalitieswithnonlipschitzmappingsandtheiroptimizationapplications-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-cho-inertialextragradientmethodsforsolvingpseudomonotonevariationalinequalitieswithnonlipschitzmappingsandtheiroptimizationapplications-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TC_ASVAO21,\nauthor={Tan, Bing and Cho, Sun Y.},\ntitle={Inertial extragradient methods for solving pseudomonotone variational inequalities with non-lipschitz mappings and their optimization applications},\njournal={Applied Set-Valued Analysis and Optimization},\nyear={2021},\nvolume={3},\nnumber={2},\npages={165--192},\ndoi={10.23952/asvao.3.2021.2.03},\nurl={https://bingtan.me/files/paper/TC-ASVAO2021.pdf},\nabstract={In this paper, four extragradient-type algorithms with inertial terms are presented for solving the variational inequality problem with a pseudomonotone and non-Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems of the suggested methods are established under some suitable conditions imposed on the parameters. Finally, several computational tests and applications in optimal control problems are given to illustrate the efficiency and advantages of the proposed iterative schemes over some known ones.},\nkeywords={Inertial extragradient method,  Non-Lipschitz operator,  Pseudomonotone operator,  Variational inequality problem,  Viscosity method},\nabbrev_source_title={Appl. Set-Valued. Anal. Optim.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, four extragradient-type algorithms with inertial terms are presented for solving the variational inequality problem with a pseudomonotone and non-Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems of the suggested methods are established under some suitable conditions imposed on the parameters. Finally, several computational tests and applications in optimal control problems are given to illustrate the efficiency and advantages of the proposed iterative schemes over some known ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-cho-aninertialmannlikealgorithmforfixedpointsofnonexpansivemappingsinhilbertspaces-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Cho, S. Y.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  An inertial mann-like algorithm for fixed points of nonexpansive mappings in Hilbert spaces.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Applied and Numerical Optimization</i>, 2(3): 335–351.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TC-JANO2020.pdf\"\n     onclick=\"log_download('tan-cho-aninertialmannlikealgorithmforfixedpointsofnonexpansivemappingsinhilbertspaces-2020', 'https://bingtan.me/files/paper/TC-JANO2020.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"An inertial mann-like algorithm for fixed points of nonexpansive mappings in Hilbert spaces [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.23952/jano.2.2020.3.05\"\n     onclick=\"log_download('tan-cho-aninertialmannlikealgorithmforfixedpointsofnonexpansivemappingsinhilbertspaces-2020', 'http://doi.org/10.23952/jano.2.2020.3.05', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-cho-aninertialmannlikealgorithmforfixedpointsofnonexpansivemappingsinhilbertspaces-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>1 download</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-cho-aninertialmannlikealgorithmforfixedpointsofnonexpansivemappingsinhilbertspaces-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TC_JANO20,\nauthor={Tan, Bing and Cho, Sun Y.},\ntitle={An inertial mann-like algorithm for fixed points of nonexpansive mappings in {H}ilbert spaces},\njournal={Journal of Applied and Numerical Optimization},\nyear={2020},\nvolume={2},\nnumber={3},\npages={335--351},\ndoi={10.23952/jano.2.2020.3.05},\nurl={https://bingtan.me/files/paper/TC-JANO2020.pdf},\nabstract={In this paper, we investigate an inertial Mann-like algorithm for fixed points of nonexpansive mappings in Hilbert spaces and obtain strong convergence results under some mild assumptions. Based on this, we derive a forward-backward algorithm involving Tikhonov regularization terms, which converges strongly to the solution of the monotone inclusion problem. We demonstrate the advantages of our algorithms comparing with some existing ones in the literature via split feasibility problem, variational inequality problem and signal recovery problem.},\nkeywords={Forward-backward splitting algorithm,  Inertial method, Mann method,  Nonexpansive mapping,  Strong convergence,  Tikhonov regularization},\nabbrev_source_title={J. Appl. Numer. Optim.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we investigate an inertial Mann-like algorithm for fixed points of nonexpansive mappings in Hilbert spaces and obtain strong convergence results under some mild assumptions. Based on this, we derive a forward-backward algorithm involving Tikhonov regularization terms, which converges strongly to the solution of the monotone inclusion problem. We demonstrate the advantages of our algorithms comparing with some existing ones in the literature via split feasibility problem, variational inequality problem and signal recovery problem.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"liu-tan-cho-ontheresolutionofvariationalinequalityproblemswithadoublehierarchicalstructure-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Liu, L.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Cho, S. Y.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  On the resolution of variational inequality problems with a double-hierarchical structure.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Nonlinear and Convex Analysis</i>, 21(2): 377–386.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><span style=\"color: red\">(ESI Highly Cited Paper)</span></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/LTC-JNCA2020.pdf\"\n     onclick=\"log_download('liu-tan-cho-ontheresolutionofvariationalinequalityproblemswithadoublehierarchicalstructure-2020', 'https://bingtan.me/files/paper/LTC-JNCA2020.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"On the resolution of variational inequality problems with a double-hierarchical structure [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/liu-tan-cho-ontheresolutionofvariationalinequalityproblemswithadoublehierarchicalstructure-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('liu-tan-cho-ontheresolutionofvariationalinequalityproblemswithadoublehierarchicalstructure-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{LTC_JNCA20,\nauthor={Liu, Liya and Tan, Bing and Cho, Sun Y.},\ntitle={On the resolution of variational inequality problems with a double-hierarchical structure},\njournal={Journal of Nonlinear and Convex Analysis},\nyear={2020},\nvolume={21},\nnumber={2},\npages={377--386},\nurl={https://bingtan.me/files/paper/LTC-JNCA2020.pdf},\nabstract={In this paper, we discuss a pseudo-monotone variational inequality problem with a variational inequality constraint over a general, nonempty, closed and convex set, which is called the double-hierarchical constrained optimization problem. In addition, we propose an iterative algorithm by incorporating inertial terms in the extragradient algorithm. Strong convergence of the algorithm to the unique solution of the problem is guaranteed under certain assumptions.},\nkeywords={Constrained optimization problem,  Inertial method, Pseudomonotone operator,  Variational inequality problem},\nabbrev_source_title={J. Nonlinear Convex Anal.},\nbibbase_note={&lt;span style=&quot;color: red&quot;&gt;(ESI Highly Cited Paper)&lt;/span&gt;},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we discuss a pseudo-monotone variational inequality problem with a variational inequality constraint over a general, nonempty, closed and convex set, which is called the double-hierarchical constrained optimization problem. In addition, we propose an iterative algorithm by incorporating inertial terms in the extragradient algorithm. Strong convergence of the algorithm to the unique solution of the problem is guaranteed under certain assumptions.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_Cho__Y_\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_Cho__Y_')\"\n      onkeypress=\"toggleGroup('group_Cho__Y_')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>Cho, Y.</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"tan-sunthrayuth-cholamjiak-cho-modifiedinertialextragradientmethodsforfindingminimumnormsolutionofthevariationalinequalityproblemwithapplicationstooptimalcontrolproblem-2023\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Sunthrayuth, P.; Cholamjiak, P.;  and Cho, Y. J.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Modified inertial extragradient methods for finding minimum-norm solution of the variational inequality problem with applications to optimal control problem.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>International Journal of Computer Mathematics</i>, 100(3): 525–545.  2023.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TSCC-IJCM23.pdf\"\n     onclick=\"log_download('tan-sunthrayuth-cholamjiak-cho-modifiedinertialextragradientmethodsforfindingminimumnormsolutionofthevariationalinequalityproblemwithapplicationstooptimalcontrolproblem-2023', 'https://bingtan.me/files/paper/TSCC-IJCM23.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Modified inertial extragradient methods for finding minimum-norm solution of the variational inequality problem with applications to optimal control problem [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1080/00207160.2022.2137672\"\n     onclick=\"log_download('tan-sunthrayuth-cholamjiak-cho-modifiedinertialextragradientmethodsforfindingminimumnormsolutionofthevariationalinequalityproblemwithapplicationstooptimalcontrolproblem-2023', 'http://doi.org/10.1080/00207160.2022.2137672', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-sunthrayuth-cholamjiak-cho-modifiedinertialextragradientmethodsforfindingminimumnormsolutionofthevariationalinequalityproblemwithapplicationstooptimalcontrolproblem-2023\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-sunthrayuth-cholamjiak-cho-modifiedinertialextragradientmethodsforfindingminimumnormsolutionofthevariationalinequalityproblemwithapplicationstooptimalcontrolproblem-2023')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TSCC_IJCM23,\nauthor={Tan, Bing and Sunthrayuth, Pongsakorn and Cholamjiak, Prasit and  Cho, Yeol J.},\ntitle={Modified inertial extragradient methods for finding minimum-norm solution of the variational inequality problem with applications to optimal control problem},\njournal={International Journal of Computer Mathematics},\nyear={2023},\nvolume={100},\nnumber={3},\npages={525--545},\ndoi={10.1080/00207160.2022.2137672},\nurl={https://bingtan.me/files/paper/TSCC-IJCM23.pdf},\nabstract={In order to discover the minimum-norm solution of the pseudomonotone variational inequality problem in a real Hilbert space, we provide two variants of the inertial extragradient approach with a novel generalized adaptive step size. Two of the suggested algorithms make use of the projection and contraction methods. We demonstrate several strong convergence findings without requiring the prior knowledge of the Lipschitz constant of the mapping. Finally, we give a number of numerical examples that highlight the benefits and effectiveness of the suggested algorithms and how they may be used to solve the optimal control problem.},\nkeywords={Variational inequality problem, Optimal control problem, Inertial method, Projection and contraction method},\nabbrev_source_title={Int. J. Comput. Math.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In order to discover the minimum-norm solution of the pseudomonotone variational inequality problem in a real Hilbert space, we provide two variants of the inertial extragradient approach with a novel generalized adaptive step size. Two of the suggested algorithms make use of the projection and contraction methods. We demonstrate several strong convergence findings without requiring the prior knowledge of the Lipschitz constant of the mapping. Finally, we give a number of numerical examples that highlight the benefits and effectiveness of the suggested algorithms and how they may be used to solve the optimal control problem.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_Cholamjiak__P_\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_Cholamjiak__P_')\"\n      onkeypress=\"toggleGroup('group_Cholamjiak__P_')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>Cholamjiak, P.</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"tan-sunthrayuth-cholamjiak-cho-modifiedinertialextragradientmethodsforfindingminimumnormsolutionofthevariationalinequalityproblemwithapplicationstooptimalcontrolproblem-2023\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Sunthrayuth, P.; Cholamjiak, P.;  and Cho, Y. J.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Modified inertial extragradient methods for finding minimum-norm solution of the variational inequality problem with applications to optimal control problem.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>International Journal of Computer Mathematics</i>, 100(3): 525–545.  2023.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TSCC-IJCM23.pdf\"\n     onclick=\"log_download('tan-sunthrayuth-cholamjiak-cho-modifiedinertialextragradientmethodsforfindingminimumnormsolutionofthevariationalinequalityproblemwithapplicationstooptimalcontrolproblem-2023', 'https://bingtan.me/files/paper/TSCC-IJCM23.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Modified inertial extragradient methods for finding minimum-norm solution of the variational inequality problem with applications to optimal control problem [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1080/00207160.2022.2137672\"\n     onclick=\"log_download('tan-sunthrayuth-cholamjiak-cho-modifiedinertialextragradientmethodsforfindingminimumnormsolutionofthevariationalinequalityproblemwithapplicationstooptimalcontrolproblem-2023', 'http://doi.org/10.1080/00207160.2022.2137672', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-sunthrayuth-cholamjiak-cho-modifiedinertialextragradientmethodsforfindingminimumnormsolutionofthevariationalinequalityproblemwithapplicationstooptimalcontrolproblem-2023\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-sunthrayuth-cholamjiak-cho-modifiedinertialextragradientmethodsforfindingminimumnormsolutionofthevariationalinequalityproblemwithapplicationstooptimalcontrolproblem-2023')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TSCC_IJCM23,\nauthor={Tan, Bing and Sunthrayuth, Pongsakorn and Cholamjiak, Prasit and  Cho, Yeol J.},\ntitle={Modified inertial extragradient methods for finding minimum-norm solution of the variational inequality problem with applications to optimal control problem},\njournal={International Journal of Computer Mathematics},\nyear={2023},\nvolume={100},\nnumber={3},\npages={525--545},\ndoi={10.1080/00207160.2022.2137672},\nurl={https://bingtan.me/files/paper/TSCC-IJCM23.pdf},\nabstract={In order to discover the minimum-norm solution of the pseudomonotone variational inequality problem in a real Hilbert space, we provide two variants of the inertial extragradient approach with a novel generalized adaptive step size. Two of the suggested algorithms make use of the projection and contraction methods. We demonstrate several strong convergence findings without requiring the prior knowledge of the Lipschitz constant of the mapping. Finally, we give a number of numerical examples that highlight the benefits and effectiveness of the suggested algorithms and how they may be used to solve the optimal control problem.},\nkeywords={Variational inequality problem, Optimal control problem, Inertial method, Projection and contraction method},\nabbrev_source_title={Int. J. Comput. Math.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In order to discover the minimum-norm solution of the pseudomonotone variational inequality problem in a real Hilbert space, we provide two variants of the inertial extragradient approach with a novel generalized adaptive step size. Two of the suggested algorithms make use of the projection and contraction methods. We demonstrate several strong convergence findings without requiring the prior knowledge of the Lipschitz constant of the mapping. Finally, we give a number of numerical examples that highlight the benefits and effectiveness of the suggested algorithms and how they may be used to solve the optimal control problem.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_Dong__Q_\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_Dong__Q_')\"\n      onkeypress=\"toggleGroup('group_Dong__Q_')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>Dong, Q.</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"zhou-cai-tan-dong-amodifiedgeneralizedversionofprojectedreflectedgradientmethodinhilbertspaces-2023\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Zhou, X.; Cai, G.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Dong, Q. L.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  A modified generalized version of projected reflected gradient method in Hilbert spaces.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Numerical Algorithms</i>, doi:10.1007/s11075-023-01566-1.  2023.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/ZCTD-NUMA2023.pdf\"\n     onclick=\"log_download('zhou-cai-tan-dong-amodifiedgeneralizedversionofprojectedreflectedgradientmethodinhilbertspaces-2023', 'https://bingtan.me/files/paper/ZCTD-NUMA2023.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"A modified generalized version of projected reflected gradient method in Hilbert spaces [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s11075-023-01566-1\"\n     onclick=\"log_download('zhou-cai-tan-dong-amodifiedgeneralizedversionofprojectedreflectedgradientmethodinhilbertspaces-2023', 'http://doi.org/10.1007/s11075-023-01566-1', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/zhou-cai-tan-dong-amodifiedgeneralizedversionofprojectedreflectedgradientmethodinhilbertspaces-2023\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('zhou-cai-tan-dong-amodifiedgeneralizedversionofprojectedreflectedgradientmethodinhilbertspaces-2023')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{ZCTD_NUMA23,\nauthor={Zhou, Xiaolin and Cai, Gang and Tan, Bing and Dong, Qiao L.},\ntitle={A modified generalized version of projected reflected gradient method in Hilbert spaces},\njournal={Numerical Algorithms},\nyear={2023},\nvolume={doi:10.1007/s11075-023-01566-1},\ndoi={10.1007/s11075-023-01566-1},\nurl={https://bingtan.me/files/paper/ZCTD-NUMA2023.pdf},\nabstract={This article is concerned with a universal version of projected reflected gradient method with new step size for solving variational inequality problem in Hilbert spaces. Under appropriate assumptions controlled by the operators and parameters, we acquire the weak convergence of the proposed algorithm. We establish an R-linear convergence rate of our method on the condition that the relevant mapping is strongly monotone. We rework our first algorithm so that it can be simplified to several generalized methods in the literature. The efficacy and availability of our proposed iterative scheme are demonstrated in numerical experiments.},\nkeywords={Projected reflected gradient method, Variational inequality, Weak and linear convergence, Hilbert spaces},\nabbrev_source_title={Numer. Algorithms},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This article is concerned with a universal version of projected reflected gradient method with new step size for solving variational inequality problem in Hilbert spaces. Under appropriate assumptions controlled by the operators and parameters, we acquire the weak convergence of the proposed algorithm. We establish an R-linear convergence rate of our method on the condition that the relevant mapping is strongly monotone. We rework our first algorithm so that it can be simplified to several generalized methods in the literature. The efficacy and availability of our proposed iterative scheme are demonstrated in numerical experiments.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_Fan__J_\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_Fan__J_')\"\n      onkeypress=\"toggleGroup('group_Fan__J_')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>Fan, J.</span>\n      <span class=\"bibbase_group_count\">\n        \n        (5)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"fan-qin-tan-tsengsextragradientalgorithmforpseudomonotonevariationalinequalitiesonhadamardmanifolds-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Fan, J.; Qin, X.;  and <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Tseng's extragradient algorithm for pseudomonotone variational inequalities on Hadamard manifolds.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Applicable Analysis</i>, 101(6): 2372–2385.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/FQT-AA2022.pdf\"\n     onclick=\"log_download('fan-qin-tan-tsengsextragradientalgorithmforpseudomonotonevariationalinequalitiesonhadamardmanifolds-2022', 'https://bingtan.me/files/paper/FQT-AA2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Tseng&#x27;s extragradient algorithm for pseudomonotone variational inequalities on Hadamard manifolds [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1080/00036811.2020.1807012\"\n     onclick=\"log_download('fan-qin-tan-tsengsextragradientalgorithmforpseudomonotonevariationalinequalitiesonhadamardmanifolds-2022', 'http://doi.org/10.1080/00036811.2020.1807012', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/fan-qin-tan-tsengsextragradientalgorithmforpseudomonotonevariationalinequalitiesonhadamardmanifolds-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('fan-qin-tan-tsengsextragradientalgorithmforpseudomonotonevariationalinequalitiesonhadamardmanifolds-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{FQT_AA22,\nauthor={Fan, Jingjing and Qin, Xiaolong and Tan, Bing},\ntitle={Tseng&#x27;s extragradient algorithm for pseudomonotone variational inequalities on {H}adamard manifolds},\njournal={Applicable Analysis},\nyear={2022},\nvolume={101},\nnumber={6},\npages={2372--2385},\ndoi={10.1080/00036811.2020.1807012},\nurl={https://bingtan.me/files/paper/FQT-AA2022.pdf},\nabstract={In this paper, we investigate the Tseng&#x27;s extragradient algorithm for non-Lipschitzian variational inequalities with pseudomonotone vector fields on Hadamard manifolds. The convergence analysis of the proposed algorithm is discussed under mild assumptions. Two experiments are provided to illustrate the asymptotical behavior of the algorithm. The results presented in this paper generalize some known results presented in the literature.},\nkeywords={Extragradient method,  Hadamard manifolds,  Non-Lipschitz operator,  Pseudomonotone vector field,  Variational inequality problem},\nabbrev_source_title={Appl. Anal.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we investigate the Tseng's extragradient algorithm for non-Lipschitzian variational inequalities with pseudomonotone vector fields on Hadamard manifolds. The convergence analysis of the proposed algorithm is discussed under mild assumptions. Two experiments are provided to illustrate the asymptotical behavior of the algorithm. The results presented in this paper generalize some known results presented in the literature.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-fan-qin-inertialextragradientalgorithmswithnonmonotonicstepsizesforsolvingvariationalinequalitiesandfixedpointproblems-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Fan, J.;  and Qin, X.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Inertial extragradient algorithms with non-monotonic step sizes for solving variational inequalities and fixed point problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Advances in Operator Theory</i>, 6(4): 61.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TFQ-AIOT2021.pdf\"\n     onclick=\"log_download('tan-fan-qin-inertialextragradientalgorithmswithnonmonotonicstepsizesforsolvingvariationalinequalitiesandfixedpointproblems-2021', 'https://bingtan.me/files/paper/TFQ-AIOT2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Inertial extragradient algorithms with non-monotonic step sizes for solving variational inequalities and fixed point problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s43036-021-00155-0\"\n     onclick=\"log_download('tan-fan-qin-inertialextragradientalgorithmswithnonmonotonicstepsizesforsolvingvariationalinequalitiesandfixedpointproblems-2021', 'http://doi.org/10.1007/s43036-021-00155-0', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-fan-qin-inertialextragradientalgorithmswithnonmonotonicstepsizesforsolvingvariationalinequalitiesandfixedpointproblems-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-fan-qin-inertialextragradientalgorithmswithnonmonotonicstepsizesforsolvingvariationalinequalitiesandfixedpointproblems-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TFQ_AIOT21,\nauthor={Tan, Bing and Fan, Jingjing and Qin, Xiaolong},\ntitle={Inertial extragradient algorithms with non-monotonic step sizes for solving variational inequalities and fixed point problems},\njournal={Advances in Operator Theory},\nyear={2021},\nvolume={6},\nnumber={4},\ndoi={10.1007/s43036-021-00155-0},\npages={61},\nurl={https://bingtan.me/files/paper/TFQ-AIOT2021.pdf},\nabstract={In this paper, we introduce four inertial extragradient algorithms with non-monotonic step sizes to find the solution of the convex feasibility problem, which consists of a monotone variational inequality problem and a fixed point problem with a demicontractive mapping. Strong convergence theorems of the suggested algorithms are established under some standard conditions. Finally, we implement some computational tests to show the efficiency and advantages of the proposed algorithms and compare them with some existing ones.},\nkeywords={Fixed point problem,  Inertial method,  Strong convergence,  Subgradient extragradient method,  Tseng&#x27;s extragradient method,  Variational inequality problem},\nabbrev_source_title={Adv. Oper. Theory},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we introduce four inertial extragradient algorithms with non-monotonic step sizes to find the solution of the convex feasibility problem, which consists of a monotone variational inequality problem and a fixed point problem with a demicontractive mapping. Strong convergence theorems of the suggested algorithms are established under some standard conditions. Finally, we implement some computational tests to show the efficiency and advantages of the proposed algorithms and compare them with some existing ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-fan-li-selfadaptiveinertialextragradientalgorithmsforsolvingvariationalinequalityproblems-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Fan, J.;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Self-adaptive inertial extragradient algorithms for solving variational inequality problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Computational and Applied Mathematics</i>, 40(1): 19.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><span style=\"color: red\">(<s>ESI Highly Cited Paper</s>)</span></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TFL-COAM2021.pdf\"\n     onclick=\"log_download('tan-fan-li-selfadaptiveinertialextragradientalgorithmsforsolvingvariationalinequalityproblems-2021', 'https://bingtan.me/files/paper/TFL-COAM2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Self-adaptive inertial extragradient algorithms for solving variational inequality problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s40314-020-01393-3\"\n     onclick=\"log_download('tan-fan-li-selfadaptiveinertialextragradientalgorithmsforsolvingvariationalinequalityproblems-2021', 'http://doi.org/10.1007/s40314-020-01393-3', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-fan-li-selfadaptiveinertialextragradientalgorithmsforsolvingvariationalinequalityproblems-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-fan-li-selfadaptiveinertialextragradientalgorithmsforsolvingvariationalinequalityproblems-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TFL_COAM21,\nauthor={Tan, Bing and Fan, Jingjing and Li, Songxiao},\ntitle={Self-adaptive inertial extragradient algorithms for solving variational inequality problems},\njournal={Computational and Applied Mathematics},\nyear={2021},\nvolume={40},\nnumber={1},\ndoi={10.1007/s40314-020-01393-3},\npages={19},\nurl={https://bingtan.me/files/paper/TFL-COAM2021.pdf},\nabstract={In this paper, we study the strong convergence of two Mann-type inertial extragradient algorithms, which are devised with a new step size, for solving a variational inequality problem with a monotone and Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems for the suggested algorithms are proved without the prior knowledge of the Lipschitz constant of the operator. Finally, we provide some numerical experiments to illustrate the performance of the proposed algorithms and provide a comparison with related ones.},\nkeywords={Inertial method,  Mann method,  Subgradient extragradient method,  Tseng&#x27;s extragradient method,  Variational inequality problem},\nabbrev_source_title={Comput. Appl. Math.},\nbibbase_note={&lt;span style=&quot;color: red&quot;&gt;(&lt;s&gt;ESI Highly Cited Paper&lt;/s&gt;)&lt;/span&gt;},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we study the strong convergence of two Mann-type inertial extragradient algorithms, which are devised with a new step size, for solving a variational inequality problem with a monotone and Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems for the suggested algorithms are proved without the prior knowledge of the Lipschitz constant of the operator. Finally, we provide some numerical experiments to illustrate the performance of the proposed algorithms and provide a comparison with related ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"fan-tan-li-anexplicitextragradientalgorithmforequilibriumproblemsonhhadamardmanifolds-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Fan, J.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  An explicit extragradient algorithm for equilibrium problems on HHadamard manifolds.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Computational and Applied Mathematics</i>, 40(2): 68.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/FTL-COAM2021.pdf\"\n     onclick=\"log_download('fan-tan-li-anexplicitextragradientalgorithmforequilibriumproblemsonhhadamardmanifolds-2021', 'https://bingtan.me/files/paper/FTL-COAM2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"An explicit extragradient algorithm for equilibrium problems on HHadamard manifolds [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s40314-021-01427-4\"\n     onclick=\"log_download('fan-tan-li-anexplicitextragradientalgorithmforequilibriumproblemsonhhadamardmanifolds-2021', 'http://doi.org/10.1007/s40314-021-01427-4', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/fan-tan-li-anexplicitextragradientalgorithmforequilibriumproblemsonhhadamardmanifolds-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('fan-tan-li-anexplicitextragradientalgorithmforequilibriumproblemsonhhadamardmanifolds-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{FTL_COAM21,\nauthor={Fan, Jingjing and Tan, Bing and Li, Songxiao},\ntitle={An explicit extragradient algorithm for equilibrium problems on {H}{H}adamard manifolds},\njournal={Computational and Applied Mathematics},\nyear={2021},\nvolume={40},\nnumber={2},\ndoi={10.1007/s40314-021-01427-4},\npages={68},\nurl={https://bingtan.me/files/paper/FTL-COAM2021.pdf},\nabstract={In this paper, we investigate a new extragradient algorithm for solving pseudomonotone equilibrium problems on Hadamard manifolds. Our algorithm uses a variable stepsize, which is updated at each iteration and based on some previous iterates. The convergence analysis of the proposed algorithm is discussed under mild assumptions. In the case where the equilibrium bifunction is strongly pseudomonotone, the R-linear rate of convergence of the new algorithm is formulated. A fundamental experiment is provided to illustrate the numerical behavior of the algorithm.},\nkeywords={Equilibrium problem,  Extragradient method,  Hadamard manifolds,  Lipschitz-type bifunction,  Pseudomonotone bifunction},\nabbrev_source_title={Comput. Appl. Math.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we investigate a new extragradient algorithm for solving pseudomonotone equilibrium problems on Hadamard manifolds. Our algorithm uses a variable stepsize, which is updated at each iteration and based on some previous iterates. The convergence analysis of the proposed algorithm is discussed under mild assumptions. In the case where the equilibrium bifunction is strongly pseudomonotone, the R-linear rate of convergence of the new algorithm is formulated. A fundamental experiment is provided to illustrate the numerical behavior of the algorithm.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"fan-qin-tan-convergenceofaninertialshadowdouglasrachfordsplittingalgorithmformonotoneinclusions-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Fan, J.; Qin, X.;  and <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Convergence of an inertial shadow Douglas-Rachford splitting algorithm for monotone inclusions.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Numerical Functional Analysis and Optimization</i>, 42(14): 1627–1644.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/FQT-NFAO2021.pdf\"\n     onclick=\"log_download('fan-qin-tan-convergenceofaninertialshadowdouglasrachfordsplittingalgorithmformonotoneinclusions-2021', 'https://bingtan.me/files/paper/FQT-NFAO2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Convergence of an inertial shadow Douglas-Rachford splitting algorithm for monotone inclusions [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1080/01630563.2021.2001749\"\n     onclick=\"log_download('fan-qin-tan-convergenceofaninertialshadowdouglasrachfordsplittingalgorithmformonotoneinclusions-2021', 'http://doi.org/10.1080/01630563.2021.2001749', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/fan-qin-tan-convergenceofaninertialshadowdouglasrachfordsplittingalgorithmformonotoneinclusions-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('fan-qin-tan-convergenceofaninertialshadowdouglasrachfordsplittingalgorithmformonotoneinclusions-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{FQT_NFAO21,\nauthor={Fan, Jingjing and Qin, Xiaolong and Tan, Bing},\ntitle={Convergence of an inertial shadow {D}ouglas-{R}achford splitting algorithm for monotone inclusions},\njournal={Numerical Functional Analysis and Optimization},\nyear={2021},\nvolume={42},\nnumber={14},\npages={1627--1644},\ndoi={10.1080/01630563.2021.2001749},\nurl={https://bingtan.me/files/paper/FQT-NFAO2021.pdf},\nabstract={An inertial shadow Douglas-Rachford splitting algorithm for finding zeros of the sum of monotone operators is proposed in Hilbert spaces. Moreover, a three-operator splitting algorithm for solving a class of monotone inclusion problems is also concerned. The weak convergence of the algorithms is investigated under mild assumptions. Some numerical experiments are implemented to illustrate our main convergence results.},\nkeywords={Inertial method,  Monotone inclusion,  Shadow Douglas-Rachford splitting algorithm,  Three-operator splitting},\nabbrev_source_title={Numer. Funct. Anal. Optim.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  An inertial shadow Douglas-Rachford splitting algorithm for finding zeros of the sum of monotone operators is proposed in Hilbert spaces. Moreover, a three-operator splitting algorithm for solving a class of monotone inclusion problems is also concerned. The weak convergence of the algorithms is investigated under mild assumptions. Some numerical experiments are implemented to illustrate our main convergence results.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_Gibali__A_\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_Gibali__A_')\"\n      onkeypress=\"toggleGroup('group_Gibali__A_')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>Gibali, A.</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"tan-qin-gibali-threeapproximationmethodsforsolvingconstraintvariationalinequalitiesandrelatedproblems-2023\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Qin, X.;  and Gibali, A.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Three approximation methods for solving constraint variational inequalities and related problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Pure and Applied Functional Analysis</i>, 8(3): 965–986.  2023.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TGQ_PAFA2023.pdf\"\n     onclick=\"log_download('tan-qin-gibali-threeapproximationmethodsforsolvingconstraintvariationalinequalitiesandrelatedproblems-2023', 'https://bingtan.me/files/paper/TGQ_PAFA2023.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Three approximation methods for solving constraint variational inequalities and related problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-qin-gibali-threeapproximationmethodsforsolvingconstraintvariationalinequalitiesandrelatedproblems-2023\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-qin-gibali-threeapproximationmethodsforsolvingconstraintvariationalinequalitiesandrelatedproblems-2023')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TGQ_PAFA23,\nauthor={Tan, Bing and Qin, Xiaolong and Gibali, Aviv},\ntitle={Three approximation methods for solving constraint variational inequalities and related problems},\njournal={Pure and Applied Functional Analysis},\nyear={2023},\nvolume={8},\nnumber={3},\npages={965--986},\nurl={https://bingtan.me/files/paper/TGQ_PAFA2023.pdf},\nabstract={In this paper, we present three new self-adaptive one-projection algorithms to find common solutions for the pseudo-monotone variational inequality problem and the fixed point problem of a demi-contractive mapping. Note that the suggested approaches use a non-monotonic self-adaptive step size so that they can work well without knowing the prior knowledge of the Lipschitz constant of the mapping. Strong convergence theorems of the proposed iterative schemes are established in real Hilbert spaces. Several mathematical experiments are reported to demonstrate the numerical behavior of the suggested algorithms and compare them with the existing ones. Finally, the suggested methods are used to solve optimal control problems.},\nkeywords={Variational inequality, Fixed point, Extragradient method, Hybrid steepest descent method, Pseudomonotone mapping},\nabbrev_source_title={Pure Appl. Funct. Anal.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we present three new self-adaptive one-projection algorithms to find common solutions for the pseudo-monotone variational inequality problem and the fixed point problem of a demi-contractive mapping. Note that the suggested approaches use a non-monotonic self-adaptive step size so that they can work well without knowing the prior knowledge of the Lipschitz constant of the mapping. Strong convergence theorems of the proposed iterative schemes are established in real Hilbert spaces. Several mathematical experiments are reported to demonstrate the numerical behavior of the suggested algorithms and compare them with the existing ones. Finally, the suggested methods are used to solve optimal control problems.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_Hu__S_\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_Hu__S_')\"\n      onkeypress=\"toggleGroup('group_Hu__S_')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>Hu, S.</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"hu-wang-tan-wang-inertialiterativemethodforsolvingvariationalinequalityproblemsofpseudomonotoneoperatorsandfixedpointproblemsofnonexpansivemappingsinhilbertspaces-2023\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Hu, S.; Wang, Y.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Wang, F.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Inertial iterative method for solving variational inequality problems of pseudo-monotone operators and fixed point problems of nonexpansive mappings in Hilbert spaces.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Industrial and Management Optimization</i>, 19(4): 2655–2675.  2023.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/HWTW-JIMO2023.pdf\"\n     onclick=\"log_download('hu-wang-tan-wang-inertialiterativemethodforsolvingvariationalinequalityproblemsofpseudomonotoneoperatorsandfixedpointproblemsofnonexpansivemappingsinhilbertspaces-2023', 'https://bingtan.me/files/paper/HWTW-JIMO2023.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Inertial iterative method for solving variational inequality problems of pseudo-monotone operators and fixed point problems of nonexpansive mappings in Hilbert spaces [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.3934/jimo.2022060\"\n     onclick=\"log_download('hu-wang-tan-wang-inertialiterativemethodforsolvingvariationalinequalityproblemsofpseudomonotoneoperatorsandfixedpointproblemsofnonexpansivemappingsinhilbertspaces-2023', 'http://doi.org/10.3934/jimo.2022060', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/hu-wang-tan-wang-inertialiterativemethodforsolvingvariationalinequalityproblemsofpseudomonotoneoperatorsandfixedpointproblemsofnonexpansivemappingsinhilbertspaces-2023\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('hu-wang-tan-wang-inertialiterativemethodforsolvingvariationalinequalityproblemsofpseudomonotoneoperatorsandfixedpointproblemsofnonexpansivemappingsinhilbertspaces-2023')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{HWTW_JIMO23,\nauthor={Hu, Shaotao and Wang, Yuanheng and Tan, Bing and Wang, Fenghui},\ntitle={Inertial iterative method for solving variational inequality problems of pseudo-monotone operators and fixed point problems of nonexpansive mappings in {H}ilbert spaces},\njournal={Journal of Industrial and Management Optimization},\nyear={2023},\nvolume={19},\nnumber={4},\npages={2655--2675},\ndoi={10.3934/jimo.2022060},\nurl={https://bingtan.me/files/paper/HWTW-JIMO2023.pdf},\nabstract={In this paper, we propose a new inertial viscosity iterative algorithm for solving the variational inequality problem with a pseudo-monotone operator and the fixed point problem involving a nonexpansive mapping in real Hilbert spaces. The advantage of the proposed algorithm is that it can work without the prior knowledge of the Lipschitz constant of the mapping. The strong convergence of the sequence generated by the proposed algorithm is proved under some suitable assumptions imposed on the parameters. Some numerical experiments are given to support our main results.},\nkeywords={Inertial method,  Viscosity method,  Strong convergence, Variational inequality problem, Fixed point problem, Nonexpansive mapping, Pseudomonotone operator},\nabbrev_source_title={J. Ind. Manag. Optim.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we propose a new inertial viscosity iterative algorithm for solving the variational inequality problem with a pseudo-monotone operator and the fixed point problem involving a nonexpansive mapping in real Hilbert spaces. The advantage of the proposed algorithm is that it can work without the prior knowledge of the Lipschitz constant of the mapping. The strong convergence of the sequence generated by the proposed algorithm is proved under some suitable assumptions imposed on the parameters. Some numerical experiments are given to support our main results.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_Latif__A_\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_Latif__A_')\"\n      onkeypress=\"toggleGroup('group_Latif__A_')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>Latif, A.</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"liu-tan-latif-approximationoffixedpointsforasemigroupofbregmanquasinonexpansivemappingsinbanachspaces-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Liu, L.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Latif, A.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Approximation of fixed points for a semigroup of Bregman quasi-nonexpansive mappings in Banach spaces.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Nonlinear and Variational Analysis</i>, 5(1): 9–22.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/LTL-JNVA2021.pdf\"\n     onclick=\"log_download('liu-tan-latif-approximationoffixedpointsforasemigroupofbregmanquasinonexpansivemappingsinbanachspaces-2021', 'https://bingtan.me/files/paper/LTL-JNVA2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Approximation of fixed points for a semigroup of Bregman quasi-nonexpansive mappings in Banach spaces [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.23952/jnva.5.2021.1.02\"\n     onclick=\"log_download('liu-tan-latif-approximationoffixedpointsforasemigroupofbregmanquasinonexpansivemappingsinbanachspaces-2021', 'http://doi.org/10.23952/jnva.5.2021.1.02', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/liu-tan-latif-approximationoffixedpointsforasemigroupofbregmanquasinonexpansivemappingsinbanachspaces-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('liu-tan-latif-approximationoffixedpointsforasemigroupofbregmanquasinonexpansivemappingsinbanachspaces-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{LTL_JNVA21,\nauthor={Liu, Liya and Tan, Bing and Latif, A.},\ntitle={Approximation of fixed points for a semigroup of Bregman quasi-nonexpansive mappings in {B}anach spaces},\njournal={Journal of Nonlinear and Variational Analysis},\nyear={2021},\nvolume={5},\nnumber={1},\npages={9--22},\ndoi={10.23952/jnva.5.2021.1.02},\nurl={https://bingtan.me/files/paper/LTL-JNVA2021.pdf},\nabstract={The purpose of this paper is to study the iterative scheme of the Halpern type for a commutative semigroup $\\mathfrak{J}=\\left\\{S_{\\lambda}: \\lambda \\in \\mathcal{Q}\\right\\}$ of Bregman quasi-nonexpansive mappings on a closed and convex subset of a Banach space. A strong convergence theorem is established for finding a common fixed point solution. Our results extend and improve some related results in the current literature. In addition, we present numerical examples to illustrate the performance of our method in finite and infinite dimensional spaces.},\nkeywords={Banach space,  Bregman quasi-nonexpansive,  Fixed point problem,  Halpern method,  Strong convergence},\nabbrev_source_title={J. Nonlinear Var. Anal.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  The purpose of this paper is to study the iterative scheme of the Halpern type for a commutative semigroup $\\mathfrak{J}=łeft\\{S_{λ}: λ ∈ \\mathcal{Q}i̊ght\\}$ of Bregman quasi-nonexpansive mappings on a closed and convex subset of a Banach space. A strong convergence theorem is established for finding a common fixed point solution. Our results extend and improve some related results in the current literature. In addition, we present numerical examples to illustrate the performance of our method in finite and infinite dimensional spaces.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_Li__S_\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_Li__S_')\"\n      onkeypress=\"toggleGroup('group_Li__S_')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>Li, S.</span>\n      <span class=\"bibbase_group_count\">\n        \n        (23)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"tan-li-cho-inertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalitieswithnonlipschitzoperatorsandapplications-2023\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Li, S.;  and Cho, S. Y.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Inertial projection and contraction methods for pseudomonotone variational inequalities with non-Lipschitz operators and applications.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Applicable Analysis</i>, 102(4): 1199–1221.  2023.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TLC-AA2023.pdf\"\n     onclick=\"log_download('tan-li-cho-inertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalitieswithnonlipschitzoperatorsandapplications-2023', 'https://bingtan.me/files/paper/TLC-AA2023.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Inertial projection and contraction methods for pseudomonotone variational inequalities with non-Lipschitz operators and applications [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1080/00036811.2021.1979219\"\n     onclick=\"log_download('tan-li-cho-inertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalitieswithnonlipschitzoperatorsandapplications-2023', 'http://doi.org/10.1080/00036811.2021.1979219', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-li-cho-inertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalitieswithnonlipschitzoperatorsandapplications-2023\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-li-cho-inertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalitieswithnonlipschitzoperatorsandapplications-2023')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TLC_AA23,\nauthor={Tan, Bing and Li, Songxiao and Cho, Sun Y.},\ntitle={Inertial projection and contraction methods for pseudomonotone variational inequalities with non-Lipschitz operators and applications},\njournal={Applicable Analysis},\nyear={2023},\nvolume={102},\nnumber={4},\ndoi={10.1080/00036811.2021.1979219},\npages={1199--1221},\nurl={https://bingtan.me/files/paper/TLC-AA2023.pdf},\nabstract={In this paper, some new accelerated iterative schemes are proposed to solve the variational inequality problem with a pseudomonotone and uniformly continuous operator in real Hilbert spaces. Strong convergence theorems of the suggested algorithms are obtained without the prior knowledge of the Lipschitz constant of the operator. Some numerical experiments and applications are performed to illustrate the advantages of the proposed methods with respect to several related ones.},\nkeywords={Inertial extragradient method,  Projection and contraction method,  Pseudomonotone operator,  Non-Lipschitz operator,  Variational inequality problem},\nabbrev_source_title={Appl. Anal.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, some new accelerated iterative schemes are proposed to solve the variational inequality problem with a pseudomonotone and uniformly continuous operator in real Hilbert spaces. Strong convergence theorems of the suggested algorithms are obtained without the prior knowledge of the Lipschitz constant of the operator. Some numerical experiments and applications are performed to illustrate the advantages of the proposed methods with respect to several related ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-li-adaptiveinertialsubgradientextragradientmethodsforfindingminimumnormsolutionsofpseudomonotonevariationalinequalities-2023\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Adaptive inertial subgradient extragradient methods for finding minimum-norm solutions of pseudomonotone variational inequalities.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Industrial and Management Optimization</i>, 19(10): 7640–7659.  2023.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TL-JIMO2023.pdf\"\n     onclick=\"log_download('tan-li-adaptiveinertialsubgradientextragradientmethodsforfindingminimumnormsolutionsofpseudomonotonevariationalinequalities-2023', 'https://bingtan.me/files/paper/TL-JIMO2023.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Adaptive inertial subgradient extragradient methods for finding minimum-norm solutions of pseudomonotone variational inequalities [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.3934/jimo.2022060\"\n     onclick=\"log_download('tan-li-adaptiveinertialsubgradientextragradientmethodsforfindingminimumnormsolutionsofpseudomonotonevariationalinequalities-2023', 'http://doi.org/10.3934/jimo.2022060', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-li-adaptiveinertialsubgradientextragradientmethodsforfindingminimumnormsolutionsofpseudomonotonevariationalinequalities-2023\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-li-adaptiveinertialsubgradientextragradientmethodsforfindingminimumnormsolutionsofpseudomonotonevariationalinequalities-2023')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TL_JIMO23,\nauthor={Tan, Bing and Li, Songxiao},\ntitle={Adaptive inertial subgradient extragradient methods for finding minimum-norm solutions of pseudomonotone variational inequalities},\njournal={Journal of Industrial and Management Optimization},\nyear={2023},\nvolume={19},\nnumber={10},\npages={7640--7659},\ndoi={10.3934/jimo.2022060},\nurl={https://bingtan.me/files/paper/TL-JIMO2023.pdf},\nabstract={In this paper, four modified inertial subgradient extragradient methods with a new non-monotonic step size criterion are investigated for pseudomonotone variational inequality problems in real Hilbert spaces. Our algorithms employ two different step sizes in each iteration to update the values of iterative sequences, and they work well without the prior information about the Lipschitz constant of the operator. Strong convergence theorems of the proposed iterative schemes are established under some suitable and mild conditions. Some numerical examples are provided to demonstrate the computational efficiency and advantages of the proposed methods over other known ones.},\nkeywords={Variational inequality problem, Inertial method, Extragradient method, Pseudomonotone operator, Non-Lipschitz operator},\nabbrev_source_title={J. Ind. Manag. Optim.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, four modified inertial subgradient extragradient methods with a new non-monotonic step size criterion are investigated for pseudomonotone variational inequality problems in real Hilbert spaces. Our algorithms employ two different step sizes in each iteration to update the values of iterative sequences, and they work well without the prior information about the Lipschitz constant of the operator. Strong convergence theorems of the proposed iterative schemes are established under some suitable and mild conditions. Some numerical examples are provided to demonstrate the computational efficiency and advantages of the proposed methods over other known ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"zhou-tan-li-inertialalgorithmswithadaptivestepsizesforsplitvariationalinclusionproblemsandtheirapplicationstosignalrecoveryproblem-2023\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Zhou, Z.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Inertial algorithms with adaptive stepsizes for split variational inclusion problems and their applications to signal recovery problem.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Mathematical Methods in the Applied Sciences</i>, doi:10.1002/mma.9436.  2023.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/ZTL-MMAS2023.pdf\"\n     onclick=\"log_download('zhou-tan-li-inertialalgorithmswithadaptivestepsizesforsplitvariationalinclusionproblemsandtheirapplicationstosignalrecoveryproblem-2023', 'https://bingtan.me/files/paper/ZTL-MMAS2023.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Inertial algorithms with adaptive stepsizes for split variational inclusion problems and their applications to signal recovery problem [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1002/mma.9436\"\n     onclick=\"log_download('zhou-tan-li-inertialalgorithmswithadaptivestepsizesforsplitvariationalinclusionproblemsandtheirapplicationstosignalrecoveryproblem-2023', 'http://doi.org/10.1002/mma.9436', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/zhou-tan-li-inertialalgorithmswithadaptivestepsizesforsplitvariationalinclusionproblemsandtheirapplicationstosignalrecoveryproblem-2023\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('zhou-tan-li-inertialalgorithmswithadaptivestepsizesforsplitvariationalinclusionproblemsandtheirapplicationstosignalrecoveryproblem-2023')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{ZTL_MMAS23,\nauthor={Zhou, Zheng and Tan, Bing and Li, Songxiao},\ntitle={Inertial algorithms with adaptive stepsizes for split variational inclusion problems and their applications to signal recovery problem},\njournal={Mathematical Methods in the Applied Sciences},\nyear={2023},\nvolume={doi:10.1002/mma.9436},\ndoi={10.1002/mma.9436},\nurl={https://bingtan.me/files/paper/ZTL-MMAS2023.pdf},\nabstract={With the help of the Meir-Keeler contraction method and the Mann-type method, two adaptive inertial iterative schemes are introduced for finding solutions of the split variational inclusion problem in Hilbert spaces. The strong convergence of the suggested algorithms is guaranteed by a new stepsize criterion that does not require calculation of the bounded linear operator norm. Some numerical experiments and applications in signal recovery problems are given to demonstrate the efficiency of the proposed algorithms.},\nkeywords={Adaptive stepsize, Inertial method, Mann method, Meir-Keeler contraction, Signal recovery, Split variational inclusion problem},\nabbrev_source_title={Math. Methods Appl. Sci.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  With the help of the Meir-Keeler contraction method and the Mann-type method, two adaptive inertial iterative schemes are introduced for finding solutions of the split variational inclusion problem in Hilbert spaces. The strong convergence of the suggested algorithms is guaranteed by a new stepsize criterion that does not require calculation of the bounded linear operator norm. Some numerical experiments and applications in signal recovery problems are given to demonstrate the efficiency of the proposed algorithms.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"luo-tan-li-inertialsplittingalgorithmsfornonlinearoperatorsofpseudocontractiveandaccretivetypes-2023\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Luo, Y.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Inertial splitting algorithms for nonlinear operators of pseudocontractive and accretive types.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Optimization</i>, 72(3): 647–675.  2023.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/LTL-OPT2023.pdf\"\n     onclick=\"log_download('luo-tan-li-inertialsplittingalgorithmsfornonlinearoperatorsofpseudocontractiveandaccretivetypes-2023', 'https://bingtan.me/files/paper/LTL-OPT2023.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Inertial splitting algorithms for nonlinear operators of pseudocontractive and accretive types [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1080/02331934.2021.1981896\"\n     onclick=\"log_download('luo-tan-li-inertialsplittingalgorithmsfornonlinearoperatorsofpseudocontractiveandaccretivetypes-2023', 'http://doi.org/10.1080/02331934.2021.1981896', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/luo-tan-li-inertialsplittingalgorithmsfornonlinearoperatorsofpseudocontractiveandaccretivetypes-2023\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('luo-tan-li-inertialsplittingalgorithmsfornonlinearoperatorsofpseudocontractiveandaccretivetypes-2023')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{LTL_OPT23,\nauthor={Luo, Yinglin and Tan, Bing and Li, Songxiao},\ntitle={Inertial splitting algorithms for nonlinear operators of pseudocontractive and accretive types},\njournal={Optimization},\nyear={2023},\nvolume={72},\nnumber={3},\npages={647--675},\ndoi={10.1080/02331934.2021.1981896},\nurl={https://bingtan.me/files/paper/LTL-OPT2023.pdf},\nabstract={In this paper, inertial splitting algorithms for nonlinear operators of pseudocontractive and accretive types are proposed. Weak and strong convergence theorems are established in uniformly convex and $q$-uniformly smooth Banach spaces. Numerical examples are given to illustrate the effectiveness of our proposed algorithms.},\nkeywords={Accretive operator,  Banach space,  Inertial method,  Strict pseudo-contraction,  Strong convergence},\nabbrev_source_title={Optimization},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, inertial splitting algorithms for nonlinear operators of pseudocontractive and accretive types are proposed. Weak and strong convergence theorems are established in uniformly convex and $q$-uniformly smooth Banach spaces. Numerical examples are given to illustrate the effectiveness of our proposed algorithms.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-li-modifiedinertialprojectionandcontractionalgorithmswithnonmonotonicstepsizesforsolvingvariationalinequalitiesandtheirapplications-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Modified inertial projection and contraction algorithms with non-monotonic step sizes for solving variational inequalities and their applications.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Optimization</i>, doi:10.1080/02331934.2022.2123705.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TL-OPT2022.pdf\"\n     onclick=\"log_download('tan-li-modifiedinertialprojectionandcontractionalgorithmswithnonmonotonicstepsizesforsolvingvariationalinequalitiesandtheirapplications-2022', 'https://bingtan.me/files/paper/TL-OPT2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Modified inertial projection and contraction algorithms with non-monotonic step sizes for solving variational inequalities and their applications [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1080/02331934.2022.2123705\"\n     onclick=\"log_download('tan-li-modifiedinertialprojectionandcontractionalgorithmswithnonmonotonicstepsizesforsolvingvariationalinequalitiesandtheirapplications-2022', 'http://doi.org/10.1080/02331934.2022.2123705', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-li-modifiedinertialprojectionandcontractionalgorithmswithnonmonotonicstepsizesforsolvingvariationalinequalitiesandtheirapplications-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-li-modifiedinertialprojectionandcontractionalgorithmswithnonmonotonicstepsizesforsolvingvariationalinequalitiesandtheirapplications-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TL_OPT22,\nauthor={Tan, Bing and Li, Songxiao},\ntitle={Modified inertial projection and contraction algorithms with non-monotonic step sizes for solving variational inequalities and their applications},\njournal={Optimization},\nyear={2022},\nvolume={doi:10.1080/02331934.2022.2123705},\ndoi={10.1080/02331934.2022.2123705},\nurl={https://bingtan.me/files/paper/TL-OPT2022.pdf},\nabstract={We present two adaptive inertial projection and contraction algorithms to discover the minimum-norm solutions of pseudomonotone variational inequality problems in real Hilbert spaces. The suggested algorithms employ two different step sizes in each iteration and use a non-monotone step size criterion without any line search allowing them to work adaptively. The strong convergence of the iterative sequences formed by the proposed algorithms is established under some mild conditions. Several numerical experiments occurring in finite- and infinite-dimensional Hilbert spaces and applications to optimal control problems as well as signal processing problems are given. Performance profiles are used to verify the computational efficiency and advantages of the proposed algorithms with respect to some known ones.},\nkeywords={Variational inequality problem,  Inertial method,  Projection and contraction method,  Subgradient extragradient method, Pseudomonotone operator, Optimal control problem, Signal processing problem, Strong convergence},\nabbrev_source_title={Optimization},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We present two adaptive inertial projection and contraction algorithms to discover the minimum-norm solutions of pseudomonotone variational inequality problems in real Hilbert spaces. The suggested algorithms employ two different step sizes in each iteration and use a non-monotone step size criterion without any line search allowing them to work adaptively. The strong convergence of the iterative sequences formed by the proposed algorithms is established under some mild conditions. Several numerical experiments occurring in finite- and infinite-dimensional Hilbert spaces and applications to optimal control problems as well as signal processing problems are given. Performance profiles are used to verify the computational efficiency and advantages of the proposed algorithms with respect to some known ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-li-revisitingprojectionandcontractionalgorithmsforsolvingvariationalinequalitiesandapplications-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Revisiting projection and contraction algorithms for solving variational inequalities and applications.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Applied Set-Valued Analysis and Optimization</i>, 4(2): 167–183.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TL-ASVAO2022.pdf\"\n     onclick=\"log_download('tan-li-revisitingprojectionandcontractionalgorithmsforsolvingvariationalinequalitiesandapplications-2022', 'https://bingtan.me/files/paper/TL-ASVAO2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Revisiting projection and contraction algorithms for solving variational inequalities and applications [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.23952/asvao.4.2022.2.03\"\n     onclick=\"log_download('tan-li-revisitingprojectionandcontractionalgorithmsforsolvingvariationalinequalitiesandapplications-2022', 'http://doi.org/10.23952/asvao.4.2022.2.03', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-li-revisitingprojectionandcontractionalgorithmsforsolvingvariationalinequalitiesandapplications-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-li-revisitingprojectionandcontractionalgorithmsforsolvingvariationalinequalitiesandapplications-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TL_ASVAO22,\nauthor={Tan, Bing and Li, Songxiao},\ntitle={Revisiting projection and contraction algorithms for solving variational inequalities and applications},\njournal={Applied Set-Valued Analysis and Optimization},\nyear={2022},\nvolume={4},\nnumber={2},\npages={167--183},\ndoi={10.23952/asvao.4.2022.2.03},\nurl={https://bingtan.me/files/paper/TL-ASVAO2022.pdf},\nabstract={We provide two novel projection and contraction algorithms to find the minimum-norm solution of the variational inequality problem with a pseudo monotone and non-Lipschitz continuous operator in a real Hilbert space. Our algorithms can work adaptively without requiring the prior information of the Lipschitz constant of the operator. Strong convergence theorems for the suggested iterative algorithms are established under suitable conditions. Some numerical experiments are discussed to demonstrate the computational efficiency of the proposed algorithms in comparison with several existing ones.},\nkeywords={Variational inequality problem, Subgradient extragradient method, Projection and contraction method, Inertial method, Pseudomonotone operator},\nabbrev_source_title={Appl. Set-Valued Anal. Optim.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We provide two novel projection and contraction algorithms to find the minimum-norm solution of the variational inequality problem with a pseudo monotone and non-Lipschitz continuous operator in a real Hilbert space. Our algorithms can work adaptively without requiring the prior information of the Lipschitz constant of the operator. Strong convergence theorems for the suggested iterative algorithms are established under suitable conditions. Some numerical experiments are discussed to demonstrate the computational efficiency of the proposed algorithms in comparison with several existing ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-zhou-li-viscositytypeinertialextragradientalgorithmsforsolvingvariationalinequalityproblemsandfixedpointproblems-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Zhou, Z.;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Viscosity-type inertial extragradient algorithms for solving variational inequality problems and fixed point problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Applied Mathematics and Computing</i>, 68(2): 1387–1411.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TZL-JAMC2022.pdf\"\n     onclick=\"log_download('tan-zhou-li-viscositytypeinertialextragradientalgorithmsforsolvingvariationalinequalityproblemsandfixedpointproblems-2022', 'https://bingtan.me/files/paper/TZL-JAMC2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Viscosity-type inertial extragradient algorithms for solving variational inequality problems and fixed point problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s12190-021-01576-z\"\n     onclick=\"log_download('tan-zhou-li-viscositytypeinertialextragradientalgorithmsforsolvingvariationalinequalityproblemsandfixedpointproblems-2022', 'http://doi.org/10.1007/s12190-021-01576-z', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-zhou-li-viscositytypeinertialextragradientalgorithmsforsolvingvariationalinequalityproblemsandfixedpointproblems-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-zhou-li-viscositytypeinertialextragradientalgorithmsforsolvingvariationalinequalityproblemsandfixedpointproblems-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TZL_JAMC22,\nauthor={Tan, Bing and Zhou, Zheng and Li, Songxiao},\ntitle={Viscosity-type inertial extragradient algorithms for solving variational inequality problems and fixed point problems},\njournal={Journal of Applied Mathematics and Computing},\nyear={2022},\nvolume={68},\nnumber={2},\npages={1387--1411},\ndoi={10.1007/s12190-021-01576-z},\nurl={https://bingtan.me/files/paper/TZL-JAMC2022.pdf},\nabstract={The paper presents two inertial viscosity-type extragradient algorithms for finding a common solution of the variational inequality problem involving a monotone and Lipschitz continuous operator and of the fixed point problem with a demicontractive mapping in real Hilbert spaces. Our algorithms use a simple step size rule which is generated by some calculations at each iteration. Two strong convergence theorems are obtained without the prior knowledge of the Lipschitz constant of the operator. The numerical behaviors of the proposed algorithms in some numerical experiments are reported and compared with previously known ones.},\nkeywords={Fixed point problem,  Inertial method,  Subgradient extragradient method,  Tseng&#x27;s extragradient method,  Variational inequality problem},\nabbrev_source_title={J. Appl. Math. Comput.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  The paper presents two inertial viscosity-type extragradient algorithms for finding a common solution of the variational inequality problem involving a monotone and Lipschitz continuous operator and of the fixed point problem with a demicontractive mapping in real Hilbert spaces. Our algorithms use a simple step size rule which is generated by some calculations at each iteration. Two strong convergence theorems are obtained without the prior knowledge of the Lipschitz constant of the operator. The numerical behaviors of the proposed algorithms in some numerical experiments are reported and compared with previously known ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-li-cho-revisitinginertialsubgradientextragradientalgorithmsforsolvingbilevelvariationalinequalityproblems-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Li, S.;  and Cho, S. Y.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Revisiting inertial subgradient extragradient algorithms for solving bilevel variational inequality problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Applied and Numerical Optimization</i>, 4(3): 425–444.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TLC-JANO2022.pdf\"\n     onclick=\"log_download('tan-li-cho-revisitinginertialsubgradientextragradientalgorithmsforsolvingbilevelvariationalinequalityproblems-2022', 'https://bingtan.me/files/paper/TLC-JANO2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Revisiting inertial subgradient extragradient algorithms for solving bilevel variational inequality problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.23952/jano.4.2022.3.08\"\n     onclick=\"log_download('tan-li-cho-revisitinginertialsubgradientextragradientalgorithmsforsolvingbilevelvariationalinequalityproblems-2022', 'http://doi.org/10.23952/jano.4.2022.3.08', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-li-cho-revisitinginertialsubgradientextragradientalgorithmsforsolvingbilevelvariationalinequalityproblems-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>1 download</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-li-cho-revisitinginertialsubgradientextragradientalgorithmsforsolvingbilevelvariationalinequalityproblems-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TLC_JANO22,\nauthor={Tan, Bing and Li, Songxiao and Cho, Sun Y.},\ntitle={Revisiting inertial subgradient extragradient algorithms for solving bilevel variational inequality problems},\njournal={Journal of Applied and Numerical Optimization},\nyear={2022},\nvolume={4},\nnumber={3},\npages={425--444},\ndoi={10.23952/jano.4.2022.3.08},\nurl={https://bingtan.me/files/paper/TLC-JANO2022.pdf},\nabstract={In this paper, four modified subgradient extragradient algorithms are proposed for solving bilevel pseudomonotone variational inequality problems in real Hilbert spaces. The proposed algorithms can work adaptively without the prior knowledge of the Lipschitz constant of the pseudomonotone mapping. Strong convergence theorems for the suggested algorithms are established under suitable and mild conditions. Finally, some numerical experiments and applications are performed to verify the efficiency of the proposed algorithms with respect to some previously known ones.},\nkeywords={Inertial method, Pseudomonotone operator, Subgradient extragradient method, Bilevel variational inequality problem},\nabbrev_source_title={J. Appl. Numer. Optim.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, four modified subgradient extragradient algorithms are proposed for solving bilevel pseudomonotone variational inequality problems in real Hilbert spaces. The proposed algorithms can work adaptively without the prior knowledge of the Lipschitz constant of the pseudomonotone mapping. Strong convergence theorems for the suggested algorithms are established under suitable and mild conditions. Finally, some numerical experiments and applications are performed to verify the efficiency of the proposed algorithms with respect to some previously known ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"zhou-tan-li-adaptivehybridsteepestdescentalgorithmsinvolvinganinertialextrapolationtermforsplitmonotonevariationalinclusionproblems-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Zhou, Z.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Adaptive hybrid steepest descent algorithms involving an inertial extrapolation term for split monotone variational inclusion problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Mathematical Methods in the Applied Sciences</i>, 45(15): 8835–8853.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/ZTL-MMAS2022.pdf\"\n     onclick=\"log_download('zhou-tan-li-adaptivehybridsteepestdescentalgorithmsinvolvinganinertialextrapolationtermforsplitmonotonevariationalinclusionproblems-2022', 'https://bingtan.me/files/paper/ZTL-MMAS2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Adaptive hybrid steepest descent algorithms involving an inertial extrapolation term for split monotone variational inclusion problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1002/mma.7931\"\n     onclick=\"log_download('zhou-tan-li-adaptivehybridsteepestdescentalgorithmsinvolvinganinertialextrapolationtermforsplitmonotonevariationalinclusionproblems-2022', 'http://doi.org/10.1002/mma.7931', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/zhou-tan-li-adaptivehybridsteepestdescentalgorithmsinvolvinganinertialextrapolationtermforsplitmonotonevariationalinclusionproblems-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>1 download</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('zhou-tan-li-adaptivehybridsteepestdescentalgorithmsinvolvinganinertialextrapolationtermforsplitmonotonevariationalinclusionproblems-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{ZTL_MMAS22,\nauthor={Zhou, Zheng and Tan, Bing and Li, Songxiao},\ntitle={Adaptive hybrid steepest descent algorithms involving an inertial extrapolation term for split monotone variational inclusion problems},\njournal={Mathematical Methods in the Applied Sciences},\nyear={2022},\nvolume={45},\nnumber={15},\npages={8835--8853},\ndoi={10.1002/mma.7931},\nurl={https://bingtan.me/files/paper/ZTL-MMAS2022.pdf},\nabstract={In this paper, we discuss the split monotone variational inclusion problem and propose two new inertial algorithms in infinite-dimensional Hilbert spaces. The iterative sequence by the proposed algorithms converges strongly to the solution of a certain variational inequality with the help of the hybrid steepest descent method. Furthermore, an adaptive step size criterion is considered in suggested algorithms to avoid the difficulty of calculating the operator norm. Meanwhile, our results are also applied to several other types of split problems. Finally, some numerical experiments show that our algorithms are realistic and summarize the known results.},\nkeywords={Adaptive stepsize,  Hybrid steepest descent method,  Inertial method,  Signal processing problem,  Strong convergence},\nabbrev_source_title={Math. Methods Appl. Sci.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we discuss the split monotone variational inclusion problem and propose two new inertial algorithms in infinite-dimensional Hilbert spaces. The iterative sequence by the proposed algorithms converges strongly to the solution of a certain variational inequality with the help of the hybrid steepest descent method. Furthermore, an adaptive step size criterion is considered in suggested algorithms to avoid the difficulty of calculating the operator norm. Meanwhile, our results are also applied to several other types of split problems. Finally, some numerical experiments show that our algorithms are realistic and summarize the known results.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"zhou-tan-li-twoselfadaptiveinertialprojectionalgorithmsforsolvingsplitvariationalinclusionproblems-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Zhou, Z.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Two self-adaptive inertial projection algorithms for solving split variational inclusion problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>AIMS Mathematics</i>, 7(4): 4960–4973.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/ZTL-AIMS2022.pdf\"\n     onclick=\"log_download('zhou-tan-li-twoselfadaptiveinertialprojectionalgorithmsforsolvingsplitvariationalinclusionproblems-2022', 'https://bingtan.me/files/paper/ZTL-AIMS2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Two self-adaptive inertial projection algorithms for solving split variational inclusion problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.3934/math.2022276\"\n     onclick=\"log_download('zhou-tan-li-twoselfadaptiveinertialprojectionalgorithmsforsolvingsplitvariationalinclusionproblems-2022', 'http://doi.org/10.3934/math.2022276', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/zhou-tan-li-twoselfadaptiveinertialprojectionalgorithmsforsolvingsplitvariationalinclusionproblems-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('zhou-tan-li-twoselfadaptiveinertialprojectionalgorithmsforsolvingsplitvariationalinclusionproblems-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{ZTL_AIMS22,\nauthor={Zhou, Zheng and Tan, Bing and Li, Songxiao},\ntitle={Two self-adaptive inertial projection algorithms for solving split variational inclusion problems},\njournal={AIMS Mathematics},\nyear={2022},\nvolume={7},\nnumber={4},\npages={4960--4973},\ndoi={10.3934/math.2022276},\nurl={https://bingtan.me/files/paper/ZTL-AIMS2022.pdf},\nabstract={This paper is to analyze the approximation solution of a split variational inclusion problem in the framework of Hilbert spaces. For this purpose, inertial hybrid and shrinking projection algorithms are proposed under the effect of a self-adaptive stepsize which does not require information of the norms of the given operators. The strong convergence properties of the proposed algorithms are obtained under mild constraints. Finally, a numerical experiment is given to illustrate the performance of proposed methods and to compare our algorithms with an existing algorithm.},\nkeywords={Inertial method,  Adaptive stepsize,  Split variational inclusion problem},\nabbrev_source_title={AIMS Math.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This paper is to analyze the approximation solution of a split variational inclusion problem in the framework of Hilbert spaces. For this purpose, inertial hybrid and shrinking projection algorithms are proposed under the effect of a self-adaptive stepsize which does not require information of the norms of the given operators. The strong convergence properties of the proposed algorithms are obtained under mild constraints. Finally, a numerical experiment is given to illustrate the performance of proposed methods and to compare our algorithms with an existing algorithm.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-li-qin-selfadaptiveinertialsingleprojectionmethodsforvariationalinequalitiesinvolvingnonlipschitzandlipschitzoperatorswiththeirapplicationstooptimalcontrolproblems-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Li, S.;  and Qin, X.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Self-adaptive inertial single projection methods for variational inequalities involving non-Lipschitz and Lipschitz operators with their applications to optimal control problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Applied Numerical Mathematics</i>, 170: 219–241.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TLQ-ANM2021.pdf\"\n     onclick=\"log_download('tan-li-qin-selfadaptiveinertialsingleprojectionmethodsforvariationalinequalitiesinvolvingnonlipschitzandlipschitzoperatorswiththeirapplicationstooptimalcontrolproblems-2021', 'https://bingtan.me/files/paper/TLQ-ANM2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Self-adaptive inertial single projection methods for variational inequalities involving non-Lipschitz and Lipschitz operators with their applications to optimal control problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1016/j.apnum.2021.07.022\"\n     onclick=\"log_download('tan-li-qin-selfadaptiveinertialsingleprojectionmethodsforvariationalinequalitiesinvolvingnonlipschitzandlipschitzoperatorswiththeirapplicationstooptimalcontrolproblems-2021', 'http://doi.org/10.1016/j.apnum.2021.07.022', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-li-qin-selfadaptiveinertialsingleprojectionmethodsforvariationalinequalitiesinvolvingnonlipschitzandlipschitzoperatorswiththeirapplicationstooptimalcontrolproblems-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-li-qin-selfadaptiveinertialsingleprojectionmethodsforvariationalinequalitiesinvolvingnonlipschitzandlipschitzoperatorswiththeirapplicationstooptimalcontrolproblems-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TLQ_ANM21,\nauthor={Tan, Bing and Li, Songxiao and Qin, Xiaolong},\ntitle={Self-adaptive inertial single projection methods for variational inequalities involving non-Lipschitz and Lipschitz operators with their applications to optimal control problems},\njournal={Applied Numerical Mathematics},\nyear={2021},\nvolume={170},\npages={219--241},\ndoi={10.1016/j.apnum.2021.07.022},\nurl={https://bingtan.me/files/paper/TLQ-ANM2021.pdf},\nabstract={In this paper, four accelerated subgradient extragradient methods are proposed to solve the variational inequality problem with a pseudo-monotone operator in real Hilbert spaces. These iterative schemes employ two new adaptive stepsize strategies that are significant when the Lipschitz constant of the mapping involved is unknown. Strong convergence theorems for the proposed algorithms are established under the condition that the operators are Lipschitz continuous and non-Lipschitz continuous. Numerical experiments on finite- and infinite-dimensional spaces and applications in optimal control problems are reported to demonstrate the advantages and efficiency of the proposed algorithms over some existing results.},\nkeywords={Inertial method, Subgradient extragradient method,  Optimal control problem,  Pseudomonotone operator,  Non-Lipschitz operator,  Variational inequality problem},\nabbrev_source_title={Appl Numer Math},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, four accelerated subgradient extragradient methods are proposed to solve the variational inequality problem with a pseudo-monotone operator in real Hilbert spaces. These iterative schemes employ two new adaptive stepsize strategies that are significant when the Lipschitz constant of the mapping involved is unknown. Strong convergence theorems for the proposed algorithms are established under the condition that the operators are Lipschitz continuous and non-Lipschitz continuous. Numerical experiments on finite- and infinite-dimensional spaces and applications in optimal control problems are reported to demonstrate the advantages and efficiency of the proposed algorithms over some existing results.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-li-qin-anacceleratedextragradientalgorithmforbilevelpseudomonotonevariationalinequalityproblemswithapplicationtooptimalcontrolproblems-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Li, S.;  and Qin, X.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  An accelerated extragradient algorithm for bilevel pseudomonotone variational inequality problems with application to optimal control problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas</i>, 115(4): 174.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TLQ-RACSAM2021.pdf\"\n     onclick=\"log_download('tan-li-qin-anacceleratedextragradientalgorithmforbilevelpseudomonotonevariationalinequalityproblemswithapplicationtooptimalcontrolproblems-2021', 'https://bingtan.me/files/paper/TLQ-RACSAM2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"An accelerated extragradient algorithm for bilevel pseudomonotone variational inequality problems with application to optimal control problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s13398-021-01116-1\"\n     onclick=\"log_download('tan-li-qin-anacceleratedextragradientalgorithmforbilevelpseudomonotonevariationalinequalityproblemswithapplicationtooptimalcontrolproblems-2021', 'http://doi.org/10.1007/s13398-021-01116-1', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-li-qin-anacceleratedextragradientalgorithmforbilevelpseudomonotonevariationalinequalityproblemswithapplicationtooptimalcontrolproblems-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-li-qin-anacceleratedextragradientalgorithmforbilevelpseudomonotonevariationalinequalityproblemswithapplicationtooptimalcontrolproblems-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TLQ_RCSM21,\nauthor={Tan, Bing and Li, Songxiao and Qin, Xiaolong},\ntitle={An accelerated extragradient algorithm for bilevel pseudomonotone variational inequality problems with application to optimal control problems},\njournal={Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas},\nyear={2021},\nvolume={115},\nnumber={4},\ndoi={10.1007/s13398-021-01116-1},\npages={174},\nurl={https://bingtan.me/files/paper/TLQ-RACSAM2021.pdf},\nabstract={In this paper, an inertial extragradient algorithm with a new non-monotonic stepsize is proposed to solve the bilevel pseudomonotone variational inequality problem in real Hilbert spaces. The advantages of the suggested iterative algorithm are that only one projection onto the feasible set needs to be performed in each iteration and the prior knowledge of the Lipschitz constant of the mapping involved does not require to be known. The strong convergence theorem of the suggested algorithm is established under some suitable conditions. Numerical experiments are reported to illustrate the advantages and efficiency of the presented algorithm over the existing related ones.},\nkeywords={Bilevel variational inequality problem,  Hybrid steepest descent method,  Inertial extragradient method,  Projection and contraction method,  Pseudomonotone operator},\nabbrev_source_title={Rev. R. Acad. Cienc. Exactas F{\\&#x27; i}s. Nat. Ser. A Mat. RACSAM},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, an inertial extragradient algorithm with a new non-monotonic stepsize is proposed to solve the bilevel pseudomonotone variational inequality problem in real Hilbert spaces. The advantages of the suggested iterative algorithm are that only one projection onto the feasible set needs to be performed in each iteration and the prior knowledge of the Lipschitz constant of the mapping involved does not require to be known. The strong convergence theorem of the suggested algorithm is established under some suitable conditions. Numerical experiments are reported to illustrate the advantages and efficiency of the presented algorithm over the existing related ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-li-qin-onmodifiedsubgradientextragradientmethodsforpseudomonotonevariationalinequalityproblemswithapplications-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Li, S.;  and Qin, X.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  On modified subgradient extragradient methods for pseudomonotone variational inequality problems with applications.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Computational and Applied Mathematics</i>, 40(7): 253.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TLQ-COAM2021.pdf\"\n     onclick=\"log_download('tan-li-qin-onmodifiedsubgradientextragradientmethodsforpseudomonotonevariationalinequalityproblemswithapplications-2021', 'https://bingtan.me/files/paper/TLQ-COAM2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"On modified subgradient extragradient methods for pseudomonotone variational inequality problems with applications [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s40314-021-01642-z\"\n     onclick=\"log_download('tan-li-qin-onmodifiedsubgradientextragradientmethodsforpseudomonotonevariationalinequalityproblemswithapplications-2021', 'http://doi.org/10.1007/s40314-021-01642-z', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-li-qin-onmodifiedsubgradientextragradientmethodsforpseudomonotonevariationalinequalityproblemswithapplications-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-li-qin-onmodifiedsubgradientextragradientmethodsforpseudomonotonevariationalinequalityproblemswithapplications-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TLQ_COAM21,\nauthor={Tan, Bing and Li, Songxiao and Qin, Xiaolong},\ntitle={On modified subgradient extragradient methods for pseudomonotone variational inequality problems with applications},\njournal={Computational and Applied Mathematics},\nyear={2021},\nvolume={40},\nnumber={7},\ndoi={10.1007/s40314-021-01642-z},\npages={253},\nurl={https://bingtan.me/files/paper/TLQ-COAM2021.pdf},\nabstract={This paper presents several modified subgradient extragradient methods with inertial effects to approximate solutions of variational inequality problems in real Hilbert spaces. The operators involved are either pseudomonotone Lipschitz continuous or pseudomonotone non-Lipschitz continuous. The advantage of the suggested algorithms is that they can work adaptively without the prior information of the Lipschitz constant of the mapping involved. Strong convergence theorems of the proposed algorithms are established under some suitable conditions. Finally, some numerical experiments are given to verify the advantages and efficiency of the proposed iterative algorithms with respect to previously known ones.},\nkeywords={Extragradient method,  Non-Lipschitz operator,  Optimal control problem,  Pseudomonotone operator,  Variational inequality problem},\nabbrev_source_title={Comput. Appl. Math.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This paper presents several modified subgradient extragradient methods with inertial effects to approximate solutions of variational inequality problems in real Hilbert spaces. The operators involved are either pseudomonotone Lipschitz continuous or pseudomonotone non-Lipschitz continuous. The advantage of the suggested algorithms is that they can work adaptively without the prior information of the Lipschitz constant of the mapping involved. Strong convergence theorems of the proposed algorithms are established under some suitable conditions. Finally, some numerical experiments are given to verify the advantages and efficiency of the proposed iterative algorithms with respect to previously known ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-fan-li-selfadaptiveinertialextragradientalgorithmsforsolvingvariationalinequalityproblems-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Fan, J.;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Self-adaptive inertial extragradient algorithms for solving variational inequality problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Computational and Applied Mathematics</i>, 40(1): 19.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><span style=\"color: red\">(<s>ESI Highly Cited Paper</s>)</span></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TFL-COAM2021.pdf\"\n     onclick=\"log_download('tan-fan-li-selfadaptiveinertialextragradientalgorithmsforsolvingvariationalinequalityproblems-2021', 'https://bingtan.me/files/paper/TFL-COAM2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Self-adaptive inertial extragradient algorithms for solving variational inequality problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s40314-020-01393-3\"\n     onclick=\"log_download('tan-fan-li-selfadaptiveinertialextragradientalgorithmsforsolvingvariationalinequalityproblems-2021', 'http://doi.org/10.1007/s40314-020-01393-3', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-fan-li-selfadaptiveinertialextragradientalgorithmsforsolvingvariationalinequalityproblems-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-fan-li-selfadaptiveinertialextragradientalgorithmsforsolvingvariationalinequalityproblems-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TFL_COAM21,\nauthor={Tan, Bing and Fan, Jingjing and Li, Songxiao},\ntitle={Self-adaptive inertial extragradient algorithms for solving variational inequality problems},\njournal={Computational and Applied Mathematics},\nyear={2021},\nvolume={40},\nnumber={1},\ndoi={10.1007/s40314-020-01393-3},\npages={19},\nurl={https://bingtan.me/files/paper/TFL-COAM2021.pdf},\nabstract={In this paper, we study the strong convergence of two Mann-type inertial extragradient algorithms, which are devised with a new step size, for solving a variational inequality problem with a monotone and Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems for the suggested algorithms are proved without the prior knowledge of the Lipschitz constant of the operator. Finally, we provide some numerical experiments to illustrate the performance of the proposed algorithms and provide a comparison with related ones.},\nkeywords={Inertial method,  Mann method,  Subgradient extragradient method,  Tseng&#x27;s extragradient method,  Variational inequality problem},\nabbrev_source_title={Comput. Appl. Math.},\nbibbase_note={&lt;span style=&quot;color: red&quot;&gt;(&lt;s&gt;ESI Highly Cited Paper&lt;/s&gt;)&lt;/span&gt;},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we study the strong convergence of two Mann-type inertial extragradient algorithms, which are devised with a new step size, for solving a variational inequality problem with a monotone and Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems for the suggested algorithms are proved without the prior knowledge of the Lipschitz constant of the operator. Finally, we provide some numerical experiments to illustrate the performance of the proposed algorithms and provide a comparison with related ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"zhou-tan-li-anacceleratedhybridprojectionmethodwithaselfadaptivestepsizesequenceforsolvingsplitcommonfixedpointproblems-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Zhou, Z.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  An accelerated hybrid projection method with a self-adaptive step-size sequence for solving split common fixed point problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Mathematical Methods in the Applied Sciences</i>, 44(8): 7294–7303.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><span style=\"color: red\">(<s>ESI Highly Cited Paper</s>)</span></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/ZTL-MMAS2021.pdf\"\n     onclick=\"log_download('zhou-tan-li-anacceleratedhybridprojectionmethodwithaselfadaptivestepsizesequenceforsolvingsplitcommonfixedpointproblems-2021', 'https://bingtan.me/files/paper/ZTL-MMAS2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"An accelerated hybrid projection method with a self-adaptive step-size sequence for solving split common fixed point problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1002/mma.7261\"\n     onclick=\"log_download('zhou-tan-li-anacceleratedhybridprojectionmethodwithaselfadaptivestepsizesequenceforsolvingsplitcommonfixedpointproblems-2021', 'http://doi.org/10.1002/mma.7261', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/zhou-tan-li-anacceleratedhybridprojectionmethodwithaselfadaptivestepsizesequenceforsolvingsplitcommonfixedpointproblems-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('zhou-tan-li-anacceleratedhybridprojectionmethodwithaselfadaptivestepsizesequenceforsolvingsplitcommonfixedpointproblems-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{ZTL_MMAS21,\nauthor={Zhou, Zheng and Tan, Bing and Li, Songxiao},\ntitle={An accelerated hybrid projection method with a self-adaptive step-size sequence for solving split common fixed point problems},\njournal={Mathematical Methods in the Applied Sciences},\nyear={2021},\nvolume={44},\nnumber={8},\npages={7294--7303},\ndoi={10.1002/mma.7261},\nurl={https://bingtan.me/files/paper/ZTL-MMAS2021.pdf},\nabstract={This paper attempts to solve the split common fixed point problem for demicontractive mappings. We give an accelerated hybrid projection algorithm that combines the hybrid projection method and the inertial technique. The strong convergence theorem of this algorithm is obtained under mild conditions by a self-adaptive step-size sequence, which does not need prior knowledge of the operator norm. Some numerical experiments in infinite-dimensional Hilbert spaces are provided to illustrate the reliability and robustness of the algorithm and also to compare it with existing ones.},\nkeywords={Demicontractive mapping,  Hybrid projection method,  Inertial method,  Split common fixed point problem},\nabbrev_source_title={Math. Methods Appl. Sci.},\nbibbase_note={&lt;span style=&quot;color: red&quot;&gt;(&lt;s&gt;ESI Highly Cited Paper&lt;/s&gt;)&lt;/span&gt;},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This paper attempts to solve the split common fixed point problem for demicontractive mappings. We give an accelerated hybrid projection algorithm that combines the hybrid projection method and the inertial technique. The strong convergence theorem of this algorithm is obtained under mild conditions by a self-adaptive step-size sequence, which does not need prior knowledge of the operator norm. Some numerical experiments in infinite-dimensional Hilbert spaces are provided to illustrate the reliability and robustness of the algorithm and also to compare it with existing ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"fan-tan-li-anexplicitextragradientalgorithmforequilibriumproblemsonhhadamardmanifolds-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Fan, J.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  An explicit extragradient algorithm for equilibrium problems on HHadamard manifolds.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Computational and Applied Mathematics</i>, 40(2): 68.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/FTL-COAM2021.pdf\"\n     onclick=\"log_download('fan-tan-li-anexplicitextragradientalgorithmforequilibriumproblemsonhhadamardmanifolds-2021', 'https://bingtan.me/files/paper/FTL-COAM2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"An explicit extragradient algorithm for equilibrium problems on HHadamard manifolds [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s40314-021-01427-4\"\n     onclick=\"log_download('fan-tan-li-anexplicitextragradientalgorithmforequilibriumproblemsonhhadamardmanifolds-2021', 'http://doi.org/10.1007/s40314-021-01427-4', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/fan-tan-li-anexplicitextragradientalgorithmforequilibriumproblemsonhhadamardmanifolds-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('fan-tan-li-anexplicitextragradientalgorithmforequilibriumproblemsonhhadamardmanifolds-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{FTL_COAM21,\nauthor={Fan, Jingjing and Tan, Bing and Li, Songxiao},\ntitle={An explicit extragradient algorithm for equilibrium problems on {H}{H}adamard manifolds},\njournal={Computational and Applied Mathematics},\nyear={2021},\nvolume={40},\nnumber={2},\ndoi={10.1007/s40314-021-01427-4},\npages={68},\nurl={https://bingtan.me/files/paper/FTL-COAM2021.pdf},\nabstract={In this paper, we investigate a new extragradient algorithm for solving pseudomonotone equilibrium problems on Hadamard manifolds. Our algorithm uses a variable stepsize, which is updated at each iteration and based on some previous iterates. The convergence analysis of the proposed algorithm is discussed under mild assumptions. In the case where the equilibrium bifunction is strongly pseudomonotone, the R-linear rate of convergence of the new algorithm is formulated. A fundamental experiment is provided to illustrate the numerical behavior of the algorithm.},\nkeywords={Equilibrium problem,  Extragradient method,  Hadamard manifolds,  Lipschitz-type bifunction,  Pseudomonotone bifunction},\nabbrev_source_title={Comput. Appl. Math.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we investigate a new extragradient algorithm for solving pseudomonotone equilibrium problems on Hadamard manifolds. Our algorithm uses a variable stepsize, which is updated at each iteration and based on some previous iterates. The convergence analysis of the proposed algorithm is discussed under mild assumptions. In the case where the equilibrium bifunction is strongly pseudomonotone, the R-linear rate of convergence of the new algorithm is formulated. A fundamental experiment is provided to illustrate the numerical behavior of the algorithm.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-li-strongconvergenceofinertialmannalgorithmsforsolvinghierarchicalfixedpointproblems-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Strong convergence of inertial mann algorithms for solving hierarchical fixed point problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Nonlinear and Variational Analysis</i>, 4(3): 337–355.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TL-JNVA2020.pdf\"\n     onclick=\"log_download('tan-li-strongconvergenceofinertialmannalgorithmsforsolvinghierarchicalfixedpointproblems-2020', 'https://bingtan.me/files/paper/TL-JNVA2020.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Strong convergence of inertial mann algorithms for solving hierarchical fixed point problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.23952/jnva.4.2020.3.02\"\n     onclick=\"log_download('tan-li-strongconvergenceofinertialmannalgorithmsforsolvinghierarchicalfixedpointproblems-2020', 'http://doi.org/10.23952/jnva.4.2020.3.02', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-li-strongconvergenceofinertialmannalgorithmsforsolvinghierarchicalfixedpointproblems-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-li-strongconvergenceofinertialmannalgorithmsforsolvinghierarchicalfixedpointproblems-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TL_JNVA20,\nauthor={Tan, Bing and Li, Songxiao},\ntitle={Strong convergence of inertial mann algorithms for solving hierarchical fixed point problems},\njournal={Journal of Nonlinear and Variational Analysis},\nyear={2020},\nvolume={4},\nnumber={3},\npages={337--355},\ndoi={10.23952/jnva.4.2020.3.02},\nurl={https://bingtan.me/files/paper/TL-JNVA2020.pdf},\nabstract={The paper introduces two inertial Mann algorithms to find solutions of hierarchical fixed point problems of nonexpansive mappings. We obtain strong convergence theorems in Hilbert spaces under suitable conditions. Some numerical examples are provided to illustrate the numerical behavior of the algorithms and numerical results show that our proposed algorithms are efficient and robust.},\nkeywords={Hierarchical fixed point problem,  Inertial method, Mann method,  Nonexpansive mapping,  Strong convergence,  Viscosity method},\nabbrev_source_title={J. Nonlinear Var. Anal.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  The paper introduces two inertial Mann algorithms to find solutions of hierarchical fixed point problems of nonexpansive mappings. We obtain strong convergence theorems in Hilbert spaces under suitable conditions. Some numerical examples are provided to illustrate the numerical behavior of the algorithms and numerical results show that our proposed algorithms are efficient and robust.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-xu-li-inertialshrinkingprojectionalgorithmsforsolvinghierarchicalvariationalinequalityproblems-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Xu, S.;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Inertial shrinking projection algorithms for solving hierarchical variational inequality problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Nonlinear and Convex Analysis</i>, 21(4): 871–884.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><span style=\"color: red\">(<s>ESI Highly Cited Paper</s>)</span></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TXL-JNCA2020.pdf\"\n     onclick=\"log_download('tan-xu-li-inertialshrinkingprojectionalgorithmsforsolvinghierarchicalvariationalinequalityproblems-2020', 'https://bingtan.me/files/paper/TXL-JNCA2020.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Inertial shrinking projection algorithms for solving hierarchical variational inequality problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-xu-li-inertialshrinkingprojectionalgorithmsforsolvinghierarchicalvariationalinequalityproblems-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-xu-li-inertialshrinkingprojectionalgorithmsforsolvinghierarchicalvariationalinequalityproblems-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TXL_JNCA20_2,\nauthor={Tan, Bing and Xu, Shanshan and Li, Songxiao},\ntitle={Inertial shrinking projection algorithms for solving hierarchical variational inequality problems},\njournal={Journal of Nonlinear and Convex Analysis},\nyear={2020},\nvolume={21},\nnumber={4},\npages={871--884},\nurl={https://bingtan.me/files/paper/TXL-JNCA2020.pdf},\nabstract={In this paper, we propose two inertial shrinking algorithms to approximate a solution of hierarchical variational inequality problems with nonex-pansive mappings in Hilbert spaces. We prove strong convergence theorems under some mild conditions. Finally, we present some numerical examples to compare our algorithms with some existing algorithms, which illustrate the advantage of our proposed algorithms.},\nkeywords={Hierarchical variational inequality problem,  Inertial method, Mann method,  Nonexpansive mapping,  Shrinking projection method,  Strong convergence},\nabbrev_source_title={J. Nonlinear Convex Anal.},\nbibbase_note={&lt;span style=&quot;color: red&quot;&gt;(&lt;s&gt;ESI Highly Cited Paper&lt;/s&gt;)&lt;/span&gt;},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we propose two inertial shrinking algorithms to approximate a solution of hierarchical variational inequality problems with nonex-pansive mappings in Hilbert spaces. We prove strong convergence theorems under some mild conditions. Finally, we present some numerical examples to compare our algorithms with some existing algorithms, which illustrate the advantage of our proposed algorithms.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-xu-li-inertialhybridandshrinkingprojectionalgorithmsforsolvingvariationalinequalityproblems-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Xu, S.;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Inertial hybrid and shrinking projection algorithms for solving variational inequality problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Nonlinear and Convex Analysis</i>, 21(10): 2193–2206.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TXL-JNCA2020-10.pdf\"\n     onclick=\"log_download('tan-xu-li-inertialhybridandshrinkingprojectionalgorithmsforsolvingvariationalinequalityproblems-2020', 'https://bingtan.me/files/paper/TXL-JNCA2020-10.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Inertial hybrid and shrinking projection algorithms for solving variational inequality problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-xu-li-inertialhybridandshrinkingprojectionalgorithmsforsolvingvariationalinequalityproblems-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-xu-li-inertialhybridandshrinkingprojectionalgorithmsforsolvingvariationalinequalityproblems-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TXL_JNCA20_1,\nauthor={Tan, Bing and Xu, Shanshan and Li, Songxiao},\ntitle={Inertial hybrid and shrinking projection algorithms for solving variational inequality problems},\njournal={Journal of Nonlinear and Convex Analysis},\nyear={2020},\nvolume={21},\nnumber={10},\npages={2193--2206},\nurl={https://bingtan.me/files/paper/TXL-JNCA2020-10.pdf},\nabstract={In this paper, we propose two inertial hybrid and shrinking projection algorithms for strict pseudo-contractions in Hilbert spaces and obtain strong theorems in general conditions. In addition, we also propose two new inertial hybrid and shrinking projection algorithms without extrapolating step for non-expansive mappings in Hilbert spaces and get strong convergence results. Finally, we give some numerical examples to illustrate the computational performance of our proposed algorithms.},\nkeywords={Variational inequality problem,  Inertial method, Hybrid projection method, Shrinking projection method, Strong convergence},\nabbrev_source_title={J. Nonlinear Convex Anal.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we propose two inertial hybrid and shrinking projection algorithms for strict pseudo-contractions in Hilbert spaces and obtain strong theorems in general conditions. In addition, we also propose two new inertial hybrid and shrinking projection algorithms without extrapolating step for non-expansive mappings in Hilbert spaces and get strong convergence results. Finally, we give some numerical examples to illustrate the computational performance of our proposed algorithms.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-xu-li-modifiedinertialhybridandshrinkingprojectionalgorithmsforsolvingfixedpointproblems-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Xu, S.;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Modified inertial hybrid and shrinking projection algorithms for solving fixed point problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Mathematics</i>, 8(2): 236.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TXL-Math2020.pdf\"\n     onclick=\"log_download('tan-xu-li-modifiedinertialhybridandshrinkingprojectionalgorithmsforsolvingfixedpointproblems-2020', 'https://bingtan.me/files/paper/TXL-Math2020.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Modified inertial hybrid and shrinking projection algorithms for solving fixed point problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.3390/math8020236\"\n     onclick=\"log_download('tan-xu-li-modifiedinertialhybridandshrinkingprojectionalgorithmsforsolvingfixedpointproblems-2020', 'http://doi.org/10.3390/math8020236', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-xu-li-modifiedinertialhybridandshrinkingprojectionalgorithmsforsolvingfixedpointproblems-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-xu-li-modifiedinertialhybridandshrinkingprojectionalgorithmsforsolvingfixedpointproblems-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TXL_MATH20,\nauthor={Tan, Bing and Xu, Shanshan and Li, Songxiao},\ntitle={Modified inertial hybrid and shrinking projection algorithms for solving fixed point problems},\njournal={Mathematics},\nyear={2020},\nvolume={8},\nnumber={2},\ndoi={10.3390/math8020236},\npages={236},\nurl={https://bingtan.me/files/paper/TXL-Math2020.pdf},\nabstract={In this paper, we introduce two modified inertial hybrid and shrinking projection algorithms for solving fixed point problems by combining the modified inertial Mann algorithm with the projection algorithm. We establish strong convergence theorems under certain suitable conditions. Finally, our algorithms are applied to convex feasibility problem, variational inequality problem, and location theory. The algorithms and results presented in this paper can summarize and unify corresponding results previously known in this field.},\nkeywords={Conjugate gradient method,  Hybrid projection method,  Inertial method,  Nonexpansive mapping,  Shrinking projection method,  Hybrid steepest descent method,  Strong convergence},\nabbrev_source_title={Mathematics},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we introduce two modified inertial hybrid and shrinking projection algorithms for solving fixed point problems by combining the modified inertial Mann algorithm with the projection algorithm. We establish strong convergence theorems under certain suitable conditions. Finally, our algorithms are applied to convex feasibility problem, variational inequality problem, and location theory. The algorithms and results presented in this paper can summarize and unify corresponding results previously known in this field.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-zhou-li-strongconvergenceofmodifiedinertialmannalgorithmsfornonexpansivemappings-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Zhou, Z.;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Strong convergence of modified inertial mann algorithms for nonexpansive mappings.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Mathematics</i>, 8(4): 462.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TZL-Math2020.pdf\"\n     onclick=\"log_download('tan-zhou-li-strongconvergenceofmodifiedinertialmannalgorithmsfornonexpansivemappings-2020', 'https://bingtan.me/files/paper/TZL-Math2020.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Strong convergence of modified inertial mann algorithms for nonexpansive mappings [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.3390/math8040462\"\n     onclick=\"log_download('tan-zhou-li-strongconvergenceofmodifiedinertialmannalgorithmsfornonexpansivemappings-2020', 'http://doi.org/10.3390/math8040462', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-zhou-li-strongconvergenceofmodifiedinertialmannalgorithmsfornonexpansivemappings-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-zhou-li-strongconvergenceofmodifiedinertialmannalgorithmsfornonexpansivemappings-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TZL_MATH20,\nauthor={Tan, Bing and Zhou, Zheng and Li, Songxiao},\ntitle={Strong convergence of modified inertial mann algorithms for nonexpansive mappings},\njournal={Mathematics},\nyear={2020},\nvolume={8},\nnumber={4},\ndoi={10.3390/math8040462},\npages={462},\nurl={https://bingtan.me/files/paper/TZL-Math2020.pdf},\nabstract={We investigated two new modified inertial Mann Halpern and inertial Mann viscosity algorithms for solving fixed point problems. Strong convergence theorems under some fewer restricted conditions are established in the framework of infinite dimensional Hilbert spaces. Finally, some numerical examples are provided to support our main results. The algorithms and results presented in this paper can generalize and extend corresponding results previously known in the literature.},\nkeywords={Halpern method,  Inertial method,  Nonexpansive mapping,  Strong convergence,  Viscosity method},\nabbrev_source_title={Mathematics},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We investigated two new modified inertial Mann Halpern and inertial Mann viscosity algorithms for solving fixed point problems. Strong convergence theorems under some fewer restricted conditions are established in the framework of infinite dimensional Hilbert spaces. Finally, some numerical examples are provided to support our main results. The algorithms and results presented in this paper can generalize and extend corresponding results previously known in the literature.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"zhou-tan-li-anewacceleratedselfadaptivestepsizealgorithmwithexcellentstabilityforsplitcommonfixedpointproblems-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Zhou, Z.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  A new accelerated self-adaptive stepsize algorithm with excellent stability for split common fixed point problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Computational and Applied Mathematics</i>, 39(3): 220.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/ZTL-COAM2020.pdf\"\n     onclick=\"log_download('zhou-tan-li-anewacceleratedselfadaptivestepsizealgorithmwithexcellentstabilityforsplitcommonfixedpointproblems-2020', 'https://bingtan.me/files/paper/ZTL-COAM2020.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"A new accelerated self-adaptive stepsize algorithm with excellent stability for split common fixed point problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s40314-020-01237-0\"\n     onclick=\"log_download('zhou-tan-li-anewacceleratedselfadaptivestepsizealgorithmwithexcellentstabilityforsplitcommonfixedpointproblems-2020', 'http://doi.org/10.1007/s40314-020-01237-0', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/zhou-tan-li-anewacceleratedselfadaptivestepsizealgorithmwithexcellentstabilityforsplitcommonfixedpointproblems-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('zhou-tan-li-anewacceleratedselfadaptivestepsizealgorithmwithexcellentstabilityforsplitcommonfixedpointproblems-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{ZTL_COAM20,\nauthor={Zhou, Zheng and Tan, Bing and Li, Songxiao},\ntitle={A new accelerated self-adaptive stepsize algorithm with excellent stability for split common fixed point problems},\njournal={Computational and Applied Mathematics},\nyear={2020},\nvolume={39},\nnumber={3},\ndoi={10.1007/s40314-020-01237-0},\npages={220},\nurl={https://bingtan.me/files/paper/ZTL-COAM2020.pdf},\nabstract={In the framework of Hilbert spaces, we study the solutions of split common fixed point problems. A new accelerated self-adaptive stepsize algorithm with excellent stability is proposed under the effects of inertial techniques and Meir–Keeler contraction mappings. The strong convergence theorems are obtained without prior knowledge of operator norms. Finally, in applications, our main results in this paper are applied to signal recovery problems.},\nkeywords={Inertial method,  Meir–Keeler contraction,  Adaptive stepsize,  Signal processing problem, Split common fixed point problem},\nabbrev_source_title={Comput. Appl. Math.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In the framework of Hilbert spaces, we study the solutions of split common fixed point problems. A new accelerated self-adaptive stepsize algorithm with excellent stability is proposed under the effects of inertial techniques and Meir–Keeler contraction mappings. The strong convergence theorems are obtained without prior knowledge of operator norms. Finally, in applications, our main results in this paper are applied to signal recovery problems.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"zhou-tan-li-aninertialshrinkingprojectionalgorithmforsplitcommonfixedpointproblems-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Zhou, Z.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  An inertial shrinking projection algorithm for split common fixed point problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Applied Analysis and Computation</i>, 10(5): 2104–2120.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/ZTL-JAAC2020.pdf\"\n     onclick=\"log_download('zhou-tan-li-aninertialshrinkingprojectionalgorithmforsplitcommonfixedpointproblems-2020', 'https://bingtan.me/files/paper/ZTL-JAAC2020.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"An inertial shrinking projection algorithm for split common fixed point problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.11948/20190330\"\n     onclick=\"log_download('zhou-tan-li-aninertialshrinkingprojectionalgorithmforsplitcommonfixedpointproblems-2020', 'http://doi.org/10.11948/20190330', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/zhou-tan-li-aninertialshrinkingprojectionalgorithmforsplitcommonfixedpointproblems-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('zhou-tan-li-aninertialshrinkingprojectionalgorithmforsplitcommonfixedpointproblems-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{ZTL_JAAC20,\nauthor={Zhou, Zheng and Tan, Bing and Li, Songxiao},\ntitle={An inertial shrinking projection algorithm for split common fixed point problems},\njournal={Journal of Applied Analysis and Computation},\nyear={2020},\nvolume={10},\nnumber={5},\npages={2104--2120},\ndoi={10.11948/20190330},\nurl={https://bingtan.me/files/paper/ZTL-JAAC2020.pdf},\nabstract={In this paper, the purpose is to introduce and study a new modified shrinking projection algorithm with inertial effects, which solves split common fixed point problems in Banach spaces. The corresponding strong convergence theorems are obtained without the assumption of semi-compactness on map-pings. Finally, some numerical examples are presented to illustrate the results in this paper.},\nkeywords={Inertial method,  Shrinking projection method,  Split common fixed point problem,  Strong convergence},\nabbrev_source_title={J. Appl. Anal. Comput.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, the purpose is to introduce and study a new modified shrinking projection algorithm with inertial effects, which solves split common fixed point problems in Banach spaces. The corresponding strong convergence theorems are obtained without the assumption of semi-compactness on map-pings. Finally, some numerical examples are presented to illustrate the results in this paper.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_Liu__L_\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_Liu__L_')\"\n      onkeypress=\"toggleGroup('group_Liu__L_')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>Liu, L.</span>\n      <span class=\"bibbase_group_count\">\n        \n        (4)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"tan-liu-qin-strongconvergenceofinertialextragradientalgorithmsforsolvingvariationalinequalitiesandfixedpointproblems-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Liu, L.;  and Qin, X.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Strong convergence of inertial extragradient algorithms for solving variational inequalities and fixed point problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Fixed Point Theory</i>, 23(2): 707–728.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TLQ-FPT2022.pdf\"\n     onclick=\"log_download('tan-liu-qin-strongconvergenceofinertialextragradientalgorithmsforsolvingvariationalinequalitiesandfixedpointproblems-2022', 'https://bingtan.me/files/paper/TLQ-FPT2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Strong convergence of inertial extragradient algorithms for solving variational inequalities and fixed point problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.24193/fpt-ro.2022.2.17\"\n     onclick=\"log_download('tan-liu-qin-strongconvergenceofinertialextragradientalgorithmsforsolvingvariationalinequalitiesandfixedpointproblems-2022', 'http://doi.org/10.24193/fpt-ro.2022.2.17', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-liu-qin-strongconvergenceofinertialextragradientalgorithmsforsolvingvariationalinequalitiesandfixedpointproblems-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-liu-qin-strongconvergenceofinertialextragradientalgorithmsforsolvingvariationalinequalitiesandfixedpointproblems-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TLQ_FPT22,\nauthor={Tan, Bing and Liu, Liya and Qin, Xiaolong},\ntitle={Strong convergence of inertial extragradient algorithms for solving variational inequalities and fixed point problems},\njournal={Fixed Point Theory},\nyear={2022},\nvolume={23},\nnumber={2},\npages={707--728},\ndoi={10.24193/fpt-ro.2022.2.17},\nurl={https://bingtan.me/files/paper/TLQ-FPT2022.pdf},\nabstract={This paper investigates two inertial extragradient algorithms for seeking a common solution to a variational inequality problem involving a monotone and Lipschitz continuous mapping and a fixed point problem with a demicontractive mapping in real Hilbert spaces. Our algorithms need to calculate the projection on the feasible set only once in each iteration. Moreover, they can work well without the prior information of the Lipschitz constant of the operator and do not contain any linesearch process. Strong convergence theorems of the suggested algorithms are established under suitable conditions. Some experiments are presented to illustrate the numerical efficiency of the suggested algorithms and compare them with some existing ones.},\nkeywords={Variational inequality problem, Fixed point problem, Subgradient extragradient method, Tseng&#x27;s extragradient method, Inertial method, Demicontractive mapping},\nabbrev_source_title={Fixed Point Theory},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This paper investigates two inertial extragradient algorithms for seeking a common solution to a variational inequality problem involving a monotone and Lipschitz continuous mapping and a fixed point problem with a demicontractive mapping in real Hilbert spaces. Our algorithms need to calculate the projection on the feasible set only once in each iteration. Moreover, they can work well without the prior information of the Lipschitz constant of the operator and do not contain any linesearch process. Strong convergence theorems of the suggested algorithms are established under suitable conditions. Some experiments are presented to illustrate the numerical efficiency of the suggested algorithms and compare them with some existing ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-liu-qin-selfadaptiveinertialextragradientalgorithmsforsolvingbilevelpseudomonotonevariationalinequalityproblems-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Liu, L.;  and Qin, X.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Self adaptive inertial extragradient algorithms for solving bilevel pseudomonotone variational inequality problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Japan Journal of Industrial and Applied Mathematics</i>, 38(2): 519-543.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><span style=\"color: red\">(<s>ESI Highly Cited Paper</s>)</span></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TLQ-JIAM2021.pdf\"\n     onclick=\"log_download('tan-liu-qin-selfadaptiveinertialextragradientalgorithmsforsolvingbilevelpseudomonotonevariationalinequalityproblems-2021', 'https://bingtan.me/files/paper/TLQ-JIAM2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Self adaptive inertial extragradient algorithms for solving bilevel pseudomonotone variational inequality problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s13160-020-00450-y\"\n     onclick=\"log_download('tan-liu-qin-selfadaptiveinertialextragradientalgorithmsforsolvingbilevelpseudomonotonevariationalinequalityproblems-2021', 'http://doi.org/10.1007/s13160-020-00450-y', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-liu-qin-selfadaptiveinertialextragradientalgorithmsforsolvingbilevelpseudomonotonevariationalinequalityproblems-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-liu-qin-selfadaptiveinertialextragradientalgorithmsforsolvingbilevelpseudomonotonevariationalinequalityproblems-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TLQ_JIAM21,\nauthor={Tan, Bing and Liu, Liya and Qin, Xiaolong},\ntitle={Self adaptive inertial extragradient algorithms for solving bilevel pseudomonotone variational inequality problems},\njournal={Japan Journal of Industrial and Applied Mathematics},\nyear={2021},\nvolume={38},\nnumber={2},\npages={519-543},\ndoi={10.1007/s13160-020-00450-y},\nurl={https://bingtan.me/files/paper/TLQ-JIAM2021.pdf},\nabstract={We introduce two inertial extragradient algorithms for solving a bilevel pseudomonotone variational inequality problem in real Hilbert spaces. The advantages of the proposed algorithms are that they can work without the prior knowledge of the Lipschitz constant of the involving operator and only one projection onto the feasible set is required. Strong convergence theorems of the suggested algorithms are obtained under suitable conditions. Finally, some numerical examples are provided to show the efficiency of the proposed algorithms.},\nkeywords={Bilevel variational inequality problem,  Inertial method, Subgradient extragradient method,  Tseng&#x27;s extragradient method,  Pseudomonotone operator,  Hybrid steepest descent method},\nabbrev_source_title={Jpn J. Ind. Appl. Math.},\nbibbase_note={&lt;span style=&quot;color: red&quot;&gt;(&lt;s&gt;ESI Highly Cited Paper&lt;/s&gt;)&lt;/span&gt;},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We introduce two inertial extragradient algorithms for solving a bilevel pseudomonotone variational inequality problem in real Hilbert spaces. The advantages of the proposed algorithms are that they can work without the prior knowledge of the Lipschitz constant of the involving operator and only one projection onto the feasible set is required. Strong convergence theorems of the suggested algorithms are obtained under suitable conditions. Finally, some numerical examples are provided to show the efficiency of the proposed algorithms.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"liu-tan-latif-approximationoffixedpointsforasemigroupofbregmanquasinonexpansivemappingsinbanachspaces-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Liu, L.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Latif, A.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Approximation of fixed points for a semigroup of Bregman quasi-nonexpansive mappings in Banach spaces.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Nonlinear and Variational Analysis</i>, 5(1): 9–22.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/LTL-JNVA2021.pdf\"\n     onclick=\"log_download('liu-tan-latif-approximationoffixedpointsforasemigroupofbregmanquasinonexpansivemappingsinbanachspaces-2021', 'https://bingtan.me/files/paper/LTL-JNVA2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Approximation of fixed points for a semigroup of Bregman quasi-nonexpansive mappings in Banach spaces [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.23952/jnva.5.2021.1.02\"\n     onclick=\"log_download('liu-tan-latif-approximationoffixedpointsforasemigroupofbregmanquasinonexpansivemappingsinbanachspaces-2021', 'http://doi.org/10.23952/jnva.5.2021.1.02', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/liu-tan-latif-approximationoffixedpointsforasemigroupofbregmanquasinonexpansivemappingsinbanachspaces-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('liu-tan-latif-approximationoffixedpointsforasemigroupofbregmanquasinonexpansivemappingsinbanachspaces-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{LTL_JNVA21,\nauthor={Liu, Liya and Tan, Bing and Latif, A.},\ntitle={Approximation of fixed points for a semigroup of Bregman quasi-nonexpansive mappings in {B}anach spaces},\njournal={Journal of Nonlinear and Variational Analysis},\nyear={2021},\nvolume={5},\nnumber={1},\npages={9--22},\ndoi={10.23952/jnva.5.2021.1.02},\nurl={https://bingtan.me/files/paper/LTL-JNVA2021.pdf},\nabstract={The purpose of this paper is to study the iterative scheme of the Halpern type for a commutative semigroup $\\mathfrak{J}=\\left\\{S_{\\lambda}: \\lambda \\in \\mathcal{Q}\\right\\}$ of Bregman quasi-nonexpansive mappings on a closed and convex subset of a Banach space. A strong convergence theorem is established for finding a common fixed point solution. Our results extend and improve some related results in the current literature. In addition, we present numerical examples to illustrate the performance of our method in finite and infinite dimensional spaces.},\nkeywords={Banach space,  Bregman quasi-nonexpansive,  Fixed point problem,  Halpern method,  Strong convergence},\nabbrev_source_title={J. Nonlinear Var. Anal.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  The purpose of this paper is to study the iterative scheme of the Halpern type for a commutative semigroup $\\mathfrak{J}=łeft\\{S_{λ}: λ ∈ \\mathcal{Q}i̊ght\\}$ of Bregman quasi-nonexpansive mappings on a closed and convex subset of a Banach space. A strong convergence theorem is established for finding a common fixed point solution. Our results extend and improve some related results in the current literature. In addition, we present numerical examples to illustrate the performance of our method in finite and infinite dimensional spaces.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"liu-tan-cho-ontheresolutionofvariationalinequalityproblemswithadoublehierarchicalstructure-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Liu, L.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Cho, S. Y.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  On the resolution of variational inequality problems with a double-hierarchical structure.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Nonlinear and Convex Analysis</i>, 21(2): 377–386.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><span style=\"color: red\">(ESI Highly Cited Paper)</span></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/LTC-JNCA2020.pdf\"\n     onclick=\"log_download('liu-tan-cho-ontheresolutionofvariationalinequalityproblemswithadoublehierarchicalstructure-2020', 'https://bingtan.me/files/paper/LTC-JNCA2020.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"On the resolution of variational inequality problems with a double-hierarchical structure [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/liu-tan-cho-ontheresolutionofvariationalinequalityproblemswithadoublehierarchicalstructure-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('liu-tan-cho-ontheresolutionofvariationalinequalityproblemswithadoublehierarchicalstructure-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{LTC_JNCA20,\nauthor={Liu, Liya and Tan, Bing and Cho, Sun Y.},\ntitle={On the resolution of variational inequality problems with a double-hierarchical structure},\njournal={Journal of Nonlinear and Convex Analysis},\nyear={2020},\nvolume={21},\nnumber={2},\npages={377--386},\nurl={https://bingtan.me/files/paper/LTC-JNCA2020.pdf},\nabstract={In this paper, we discuss a pseudo-monotone variational inequality problem with a variational inequality constraint over a general, nonempty, closed and convex set, which is called the double-hierarchical constrained optimization problem. In addition, we propose an iterative algorithm by incorporating inertial terms in the extragradient algorithm. Strong convergence of the algorithm to the unique solution of the problem is guaranteed under certain assumptions.},\nkeywords={Constrained optimization problem,  Inertial method, Pseudomonotone operator,  Variational inequality problem},\nabbrev_source_title={J. Nonlinear Convex Anal.},\nbibbase_note={&lt;span style=&quot;color: red&quot;&gt;(ESI Highly Cited Paper)&lt;/span&gt;},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we discuss a pseudo-monotone variational inequality problem with a variational inequality constraint over a general, nonempty, closed and convex set, which is called the double-hierarchical constrained optimization problem. In addition, we propose an iterative algorithm by incorporating inertial terms in the extragradient algorithm. Strong convergence of the algorithm to the unique solution of the problem is guaranteed under certain assumptions.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_Luo__Y_\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_Luo__Y_')\"\n      onkeypress=\"toggleGroup('group_Luo__Y_')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>Luo, Y.</span>\n      <span class=\"bibbase_group_count\">\n        \n        (2)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"luo-tan-li-inertialsplittingalgorithmsfornonlinearoperatorsofpseudocontractiveandaccretivetypes-2023\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Luo, Y.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Inertial splitting algorithms for nonlinear operators of pseudocontractive and accretive types.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Optimization</i>, 72(3): 647–675.  2023.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/LTL-OPT2023.pdf\"\n     onclick=\"log_download('luo-tan-li-inertialsplittingalgorithmsfornonlinearoperatorsofpseudocontractiveandaccretivetypes-2023', 'https://bingtan.me/files/paper/LTL-OPT2023.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Inertial splitting algorithms for nonlinear operators of pseudocontractive and accretive types [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1080/02331934.2021.1981896\"\n     onclick=\"log_download('luo-tan-li-inertialsplittingalgorithmsfornonlinearoperatorsofpseudocontractiveandaccretivetypes-2023', 'http://doi.org/10.1080/02331934.2021.1981896', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/luo-tan-li-inertialsplittingalgorithmsfornonlinearoperatorsofpseudocontractiveandaccretivetypes-2023\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('luo-tan-li-inertialsplittingalgorithmsfornonlinearoperatorsofpseudocontractiveandaccretivetypes-2023')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{LTL_OPT23,\nauthor={Luo, Yinglin and Tan, Bing and Li, Songxiao},\ntitle={Inertial splitting algorithms for nonlinear operators of pseudocontractive and accretive types},\njournal={Optimization},\nyear={2023},\nvolume={72},\nnumber={3},\npages={647--675},\ndoi={10.1080/02331934.2021.1981896},\nurl={https://bingtan.me/files/paper/LTL-OPT2023.pdf},\nabstract={In this paper, inertial splitting algorithms for nonlinear operators of pseudocontractive and accretive types are proposed. Weak and strong convergence theorems are established in uniformly convex and $q$-uniformly smooth Banach spaces. Numerical examples are given to illustrate the effectiveness of our proposed algorithms.},\nkeywords={Accretive operator,  Banach space,  Inertial method,  Strict pseudo-contraction,  Strong convergence},\nabbrev_source_title={Optimization},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, inertial splitting algorithms for nonlinear operators of pseudocontractive and accretive types are proposed. Weak and strong convergence theorems are established in uniformly convex and $q$-uniformly smooth Banach spaces. Numerical examples are given to illustrate the effectiveness of our proposed algorithms.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"luo-shang-tan-ageneralinertialviscositytypemethodfornonexpansivemappingsanditsapplicationsinsignalprocessing-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Luo, Y.; Shang, M.;  and <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  A general inertial viscosity type method for nonexpansive mappings and its applications in signal processing.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Mathematics</i>, 8(2): 288.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/LST-Math2020.pdf\"\n     onclick=\"log_download('luo-shang-tan-ageneralinertialviscositytypemethodfornonexpansivemappingsanditsapplicationsinsignalprocessing-2020', 'https://bingtan.me/files/paper/LST-Math2020.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"A general inertial viscosity type method for nonexpansive mappings and its applications in signal processing [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.3390/math8020288\"\n     onclick=\"log_download('luo-shang-tan-ageneralinertialviscositytypemethodfornonexpansivemappingsanditsapplicationsinsignalprocessing-2020', 'http://doi.org/10.3390/math8020288', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/luo-shang-tan-ageneralinertialviscositytypemethodfornonexpansivemappingsanditsapplicationsinsignalprocessing-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('luo-shang-tan-ageneralinertialviscositytypemethodfornonexpansivemappingsanditsapplicationsinsignalprocessing-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{LST_MATH20,\nauthor={Luo, Yinglin and Shang, Meijuan and Tan, Bing},\ntitle={A general inertial viscosity type method for nonexpansive mappings and its applications in signal processing},\njournal={Mathematics},\nyear={2020},\nvolume={8},\nnumber={2},\ndoi={10.3390/math8020288},\npages={288},\nurl={https://bingtan.me/files/paper/LST-Math2020.pdf},\nabstract={In this paper, we propose viscosity algorithms with two different inertia parameters for solving fixed points of nonexpansive and strictly pseudocontractive mappings. Strong convergence theorems are obtained in Hilbert spaces and the applications to the signal processing are considered. Moreover, some numerical experiments of proposed algorithms and comparisons with existing algorithms are given to the demonstration of the efficiency of the proposed algorithms. The numerical results show that our algorithms are superior to some related algorithms.},\nkeywords={Inclusion problem,  Nonexpansive mapping,  Signal processing problem,  Strict pseudo-contraction,  Variational inequality problem},\nabbrev_source_title={Mathematics},\n}\n\n\n\n\n\n\n\n\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we propose viscosity algorithms with two different inertia parameters for solving fixed points of nonexpansive and strictly pseudocontractive mappings. Strong convergence theorems are obtained in Hilbert spaces and the applications to the signal processing are considered. Moreover, some numerical experiments of proposed algorithms and comparisons with existing algorithms are given to the demonstration of the efficiency of the proposed algorithms. The numerical results show that our algorithms are superior to some related algorithms.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_Petru_el__A_\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_Petru_el__A_')\"\n      onkeypress=\"toggleGroup('group_Petru_el__A_')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>Petruşel, A.</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"tan-petruel-qin-yao-globalandlinearconvergenceofalternatedinertialsingleprojectionalgorithmsforpseudomonotonevariationalinequalities-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Petruşel, A.; Qin, X.;  and Yao, J. C.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Global and linear convergence of alternated inertial single projection algorithms for pseudo-monotone variational inequalities.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Fixed Point Theory</i>, 23(1): 391–426.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TPQY-FPT2022.pdf\"\n     onclick=\"log_download('tan-petruel-qin-yao-globalandlinearconvergenceofalternatedinertialsingleprojectionalgorithmsforpseudomonotonevariationalinequalities-2022', 'https://bingtan.me/files/paper/TPQY-FPT2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Global and linear convergence of alternated inertial single projection algorithms for pseudo-monotone variational inequalities [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.24193/fpt-ro.2022.1.25\"\n     onclick=\"log_download('tan-petruel-qin-yao-globalandlinearconvergenceofalternatedinertialsingleprojectionalgorithmsforpseudomonotonevariationalinequalities-2022', 'http://doi.org/10.24193/fpt-ro.2022.1.25', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-petruel-qin-yao-globalandlinearconvergenceofalternatedinertialsingleprojectionalgorithmsforpseudomonotonevariationalinequalities-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>2 downloads</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-petruel-qin-yao-globalandlinearconvergenceofalternatedinertialsingleprojectionalgorithmsforpseudomonotonevariationalinequalities-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TPQY_FPT22,\nauthor={Tan, Bing and Petruşel, Adrian and Qin, Xiaolong and Yao, Jen C.},\ntitle={Global and linear convergence of alternated inertial single projection algorithms for pseudo-monotone variational inequalities},\njournal={Fixed Point Theory},\nyear={2022},\nvolume={23},\nnumber={1},\npages={391--426},\ndoi={10.24193/fpt-ro.2022.1.25},\nurl={https://bingtan.me/files/paper/TPQY-FPT2022.pdf},\nabstract={In this paper, we investigate three new relaxed single projection methods with alternating inertial extrapolation steps and adaptive non-monotonic step sizes for solving pseudo-monotone variational inequalities in real Hilbert spaces. The proposed algorithms need to compute the projection on the feasible set only once in each iteration and they can work adaptively without the prior information of the Lipschitz constant of the mapping. The weak convergence theorems of the proposed iterative schemes are established under some appropriate conditions imposed on the parameters. These methods recover the Fejér monotonicity of the even subsequence with respect to the solution and obtain linear convergence rates. Finally, some numerical experiments and applications to optimal control problems are provided to demonstrate the advantages and efficiency of the proposed methods compared to some recent related ones.},\nkeywords={Adaptive stepsize,  Alternated inertial method,  Projection and contraction method,  Pseudomonotone operator,  Subgradient extragradient method,  Variational inequality problem},\nabbrev_source_title={Fixed Point Theory},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we investigate three new relaxed single projection methods with alternating inertial extrapolation steps and adaptive non-monotonic step sizes for solving pseudo-monotone variational inequalities in real Hilbert spaces. The proposed algorithms need to compute the projection on the feasible set only once in each iteration and they can work adaptively without the prior information of the Lipschitz constant of the mapping. The weak convergence theorems of the proposed iterative schemes are established under some appropriate conditions imposed on the parameters. These methods recover the Fejér monotonicity of the even subsequence with respect to the solution and obtain linear convergence rates. Finally, some numerical experiments and applications to optimal control problems are provided to demonstrate the advantages and efficiency of the proposed methods compared to some recent related ones.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_Qin__X_\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_Qin__X_')\"\n      onkeypress=\"toggleGroup('group_Qin__X_')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>Qin, X.</span>\n      <span class=\"bibbase_group_count\">\n        \n        (20)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"tan-qin-wang-alternatedinertialalgorithmsforsplitfeasibilityproblems-2024\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Qin, X.;  and Wang, X.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Alternated inertial algorithms for split feasibility problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Numerical Algorithms</i>, 95(2): 773–812.  2024.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TQW-NUMA2024.pdf\"\n     onclick=\"log_download('tan-qin-wang-alternatedinertialalgorithmsforsplitfeasibilityproblems-2024', 'https://bingtan.me/files/paper/TQW-NUMA2024.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Alternated inertial algorithms for split feasibility problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s11075-023-01589-8\"\n     onclick=\"log_download('tan-qin-wang-alternatedinertialalgorithmsforsplitfeasibilityproblems-2024', 'http://doi.org/10.1007/s11075-023-01589-8', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-qin-wang-alternatedinertialalgorithmsforsplitfeasibilityproblems-2024\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-qin-wang-alternatedinertialalgorithmsforsplitfeasibilityproblems-2024')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TQW_NUMA24,\nauthor={Tan, Bing and Qin, Xiaolong and Wang, Xianfu},\ntitle={Alternated inertial algorithms for split feasibility problems},\njournal={Numerical Algorithms},\nyear={2024},\nvolume={95},\nnumber={2},\npages={773--812},\ndoi={10.1007/s11075-023-01589-8},\nurl={https://bingtan.me/files/paper/TQW-NUMA2024.pdf},\nabstract={We introduce four novel relaxed CQ algorithms with alternating inertial for solving split feasibility problems in real Hilbert spaces. The proposed algorithms employ a new non-monotonic adaptive step size criterion and utilize two different step sizes in each iteration. The weak convergence of the iterative sequences generated by the proposed algorithms is established under some weak conditions. Moreover, the Fejér monotonicity of the even subsequence with respect to the solution set is recovered. Two applications in signal denoising and image deblurring are given to illustrate the computational efficiency of our algorithms.},\nkeywords={Split feasibility problem,  CQ method,  Projection and contraction method,  Alternated inertial method,  Signal processing,  Image restoration},\nabbrev_source_title={Numer. Algorithms},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We introduce four novel relaxed CQ algorithms with alternating inertial for solving split feasibility problems in real Hilbert spaces. The proposed algorithms employ a new non-monotonic adaptive step size criterion and utilize two different step sizes in each iteration. The weak convergence of the iterative sequences generated by the proposed algorithms is established under some weak conditions. Moreover, the Fejér monotonicity of the even subsequence with respect to the solution set is recovered. Two applications in signal denoising and image deblurring are given to illustrate the computational efficiency of our algorithms.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-qin-analternatedinertialalgorithmwithweakandlinearconvergenceforsolvingmonotoneinclusions-2023\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Qin, X.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  An alternated inertial algorithm with weak and linear convergence for solving monotone inclusions.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Annals of Mathematical Sciences and Applications</i>, 8(2): 321–345.  2023.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TQ-AMSA2023.pdf\"\n     onclick=\"log_download('tan-qin-analternatedinertialalgorithmwithweakandlinearconvergenceforsolvingmonotoneinclusions-2023', 'https://bingtan.me/files/paper/TQ-AMSA2023.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"An alternated inertial algorithm with weak and linear convergence for solving monotone inclusions [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.4310/AMSA.2023.v8.n2.a7\"\n     onclick=\"log_download('tan-qin-analternatedinertialalgorithmwithweakandlinearconvergenceforsolvingmonotoneinclusions-2023', 'http://doi.org/10.4310/AMSA.2023.v8.n2.a7', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-qin-analternatedinertialalgorithmwithweakandlinearconvergenceforsolvingmonotoneinclusions-2023\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-qin-analternatedinertialalgorithmwithweakandlinearconvergenceforsolvingmonotoneinclusions-2023')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TQ_AMSA23,\nauthor={Tan, Bing and Qin, Xiaolong},\ntitle={An alternated inertial algorithm with weak and linear convergence for solving monotone inclusions},\njournal={Annals of Mathematical Sciences and Applications},\nyear={2023},\nvolume={8},\nnumber={2},\npages={321--345},\ndoi={10.4310/AMSA.2023.v8.n2.a7},\nurl={https://bingtan.me/files/paper/TQ-AMSA2023.pdf},\nabstract={Inertial-based methods have the drawback of not preserving the Fejér monotonicity of iterative sequences, which may result in slower convergence compared to their corresponding non-inertial versions. To overcome this issue, Mu and Peng [Stat. Optim. Inf. Comput. 3 (2015), 241–248; MR3393305] suggested an alternating inertial method that can recover the Fejér monotonicity of even subsequences. In this paper, we propose a modified version of the forward-backward algorithm with alternating inertial and relaxation effects to solve an inclusion problem in real Hilbert spaces. The weak and linear convergence of the presented algorithm is established under suitable and mild conditions on the involved operators and parameters. Furthermore, the Fejér monotonicity of even subsequences generated by the proposed algorithm with respect to the solution set is recovered. Finally, our tests on image restoration problems demonstrate the superiority of the proposed algorithm over some related results.},\nkeywords={Inclusion problems, Alternated inertial, Forward-backward method, Tseng&#x27;s method, Projection and contraction method, Linear convergence},\nabbrev_source_title={Ann. Math. Sci. Appl.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  Inertial-based methods have the drawback of not preserving the Fejér monotonicity of iterative sequences, which may result in slower convergence compared to their corresponding non-inertial versions. To overcome this issue, Mu and Peng [Stat. Optim. Inf. Comput. 3 (2015), 241–248; MR3393305] suggested an alternating inertial method that can recover the Fejér monotonicity of even subsequences. In this paper, we propose a modified version of the forward-backward algorithm with alternating inertial and relaxation effects to solve an inclusion problem in real Hilbert spaces. The weak and linear convergence of the presented algorithm is established under suitable and mild conditions on the involved operators and parameters. Furthermore, the Fejér monotonicity of even subsequences generated by the proposed algorithm with respect to the solution set is recovered. Finally, our tests on image restoration problems demonstrate the superiority of the proposed algorithm over some related results.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-qin-gibali-threeapproximationmethodsforsolvingconstraintvariationalinequalitiesandrelatedproblems-2023\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Qin, X.;  and Gibali, A.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Three approximation methods for solving constraint variational inequalities and related problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Pure and Applied Functional Analysis</i>, 8(3): 965–986.  2023.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TGQ_PAFA2023.pdf\"\n     onclick=\"log_download('tan-qin-gibali-threeapproximationmethodsforsolvingconstraintvariationalinequalitiesandrelatedproblems-2023', 'https://bingtan.me/files/paper/TGQ_PAFA2023.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Three approximation methods for solving constraint variational inequalities and related problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-qin-gibali-threeapproximationmethodsforsolvingconstraintvariationalinequalitiesandrelatedproblems-2023\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-qin-gibali-threeapproximationmethodsforsolvingconstraintvariationalinequalitiesandrelatedproblems-2023')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TGQ_PAFA23,\nauthor={Tan, Bing and Qin, Xiaolong and Gibali, Aviv},\ntitle={Three approximation methods for solving constraint variational inequalities and related problems},\njournal={Pure and Applied Functional Analysis},\nyear={2023},\nvolume={8},\nnumber={3},\npages={965--986},\nurl={https://bingtan.me/files/paper/TGQ_PAFA2023.pdf},\nabstract={In this paper, we present three new self-adaptive one-projection algorithms to find common solutions for the pseudo-monotone variational inequality problem and the fixed point problem of a demi-contractive mapping. Note that the suggested approaches use a non-monotonic self-adaptive step size so that they can work well without knowing the prior knowledge of the Lipschitz constant of the mapping. Strong convergence theorems of the proposed iterative schemes are established in real Hilbert spaces. Several mathematical experiments are reported to demonstrate the numerical behavior of the suggested algorithms and compare them with the existing ones. Finally, the suggested methods are used to solve optimal control problems.},\nkeywords={Variational inequality, Fixed point, Extragradient method, Hybrid steepest descent method, Pseudomonotone mapping},\nabbrev_source_title={Pure Appl. Funct. Anal.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we present three new self-adaptive one-projection algorithms to find common solutions for the pseudo-monotone variational inequality problem and the fixed point problem of a demi-contractive mapping. Note that the suggested approaches use a non-monotonic self-adaptive step size so that they can work well without knowing the prior knowledge of the Lipschitz constant of the mapping. Strong convergence theorems of the proposed iterative schemes are established in real Hilbert spaces. Several mathematical experiments are reported to demonstrate the numerical behavior of the suggested algorithms and compare them with the existing ones. Finally, the suggested methods are used to solve optimal control problems.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-qin-cho-revisitingsubgradientextragradientmethodsforsolvingvariationalinequalities-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Qin, X.;  and Cho, S. Y.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Revisiting subgradient extragradient methods for solving variational inequalities.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Numerical Algorithms</i>, 90(4): 1593–1615.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TQC-NUMA2022.pdf\"\n     onclick=\"log_download('tan-qin-cho-revisitingsubgradientextragradientmethodsforsolvingvariationalinequalities-2022', 'https://bingtan.me/files/paper/TQC-NUMA2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Revisiting subgradient extragradient methods for solving variational inequalities [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s11075-021-01243-1\"\n     onclick=\"log_download('tan-qin-cho-revisitingsubgradientextragradientmethodsforsolvingvariationalinequalities-2022', 'http://doi.org/10.1007/s11075-021-01243-1', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-qin-cho-revisitingsubgradientextragradientmethodsforsolvingvariationalinequalities-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>2 downloads</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-qin-cho-revisitingsubgradientextragradientmethodsforsolvingvariationalinequalities-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TQC_NUMA22,\nauthor={Tan, Bing and Qin, Xiaolong and Cho, Sun Y.},\ntitle={Revisiting subgradient extragradient methods for solving variational inequalities},\njournal={Numerical Algorithms},\nyear={2022},\nvolume={90},\nnumber={4},\npages={1593--1615},\ndoi={10.1007/s11075-021-01243-1},\nurl={https://bingtan.me/files/paper/TQC-NUMA2022.pdf},\nabstract={In this paper, several extragradient algorithms with inertial effects and adaptive non-monotonic step sizes are proposed to solve pseudomonotone variational inequalities in real Hilbert spaces. The strong convergence of the proposed methods is established without the prior knowledge of the Lipschitz constant of the mapping. Some numerical experiments are given to illustrate the advantages and efficiency of the proposed schemes over previously known ones.},\nkeywords={Armijo stepsize,  Inertial extragradient method,  Non-Lipschitz operator,  Pseudomonotone operator,  Variational inequality problem},\nabbrev_source_title={Numer. Algorithms},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, several extragradient algorithms with inertial effects and adaptive non-monotonic step sizes are proposed to solve pseudomonotone variational inequalities in real Hilbert spaces. The strong convergence of the proposed methods is established without the prior knowledge of the Lipschitz constant of the mapping. Some numerical experiments are given to illustrate the advantages and efficiency of the proposed schemes over previously known ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-qin-yao-strongconvergenceofinertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalitieswithapplicationstooptimalcontrolproblems-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Qin, X.;  and Yao, J. C.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Strong convergence of inertial projection and contraction methods for pseudomonotone variational inequalities with applications to optimal control problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Global Optimization</i>, 82(3): 523–557.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TQY-JOGO2022.pdf\"\n     onclick=\"log_download('tan-qin-yao-strongconvergenceofinertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalitieswithapplicationstooptimalcontrolproblems-2022', 'https://bingtan.me/files/paper/TQY-JOGO2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Strong convergence of inertial projection and contraction methods for pseudomonotone variational inequalities with applications to optimal control problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s10898-021-01095-y\"\n     onclick=\"log_download('tan-qin-yao-strongconvergenceofinertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalitieswithapplicationstooptimalcontrolproblems-2022', 'http://doi.org/10.1007/s10898-021-01095-y', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-qin-yao-strongconvergenceofinertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalitieswithapplicationstooptimalcontrolproblems-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-qin-yao-strongconvergenceofinertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalitieswithapplicationstooptimalcontrolproblems-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TQY_JOGO22,\nauthor={Tan, Bing and Qin, Xiaolong and Yao, Jen C.},\ntitle={Strong convergence of inertial projection and contraction methods for pseudomonotone variational inequalities with applications to optimal control problems},\njournal={Journal of Global Optimization},\nyear={2022},\nvolume={82},\nnumber={3},\npages={523--557},\ndoi={10.1007/s10898-021-01095-y},\nurl={https://bingtan.me/files/paper/TQY-JOGO2022.pdf},\nabstract={This paper investigates some inertial projection and contraction methods for solving pseudomonotone variational inequality problems in real Hilbert spaces. The algorithms use a new non-monotonic step size so that they can work without the prior knowledge of the Lipschitz constant of the operator. Strong convergence theorems of the suggested algorithms are obtained under some suitable conditions. Some numerical experiments in finite- and infinite-dimensional spaces and applications in optimal control problems are implemented to demonstrate the performance of the suggested schemes and we also compare them with several related results.},\nkeywords={Inertial method,  Optimal control problem,  Projection and contraction method,  Pseudomonotone operator,  Subgradient extragradient method,  Variational inequality problem},\nabbrev_source_title={J. Global Optim.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This paper investigates some inertial projection and contraction methods for solving pseudomonotone variational inequality problems in real Hilbert spaces. The algorithms use a new non-monotonic step size so that they can work without the prior knowledge of the Lipschitz constant of the operator. Strong convergence theorems of the suggested algorithms are obtained under some suitable conditions. Some numerical experiments in finite- and infinite-dimensional spaces and applications in optimal control problems are implemented to demonstrate the performance of the suggested schemes and we also compare them with several related results.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-qin-modifiedinertialprojectionandcontractionalgorithmsforsolvingvariationalinequalityproblemswithnonlipschitzcontinuousoperators-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Qin, X.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Modified inertial projection and contraction algorithms for solving variational inequality problems with non-Lipschitz continuous operators.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Analysis and Mathematical Physics</i>, 12(1): 26.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TQ-AMP2022.pdf\"\n     onclick=\"log_download('tan-qin-modifiedinertialprojectionandcontractionalgorithmsforsolvingvariationalinequalityproblemswithnonlipschitzcontinuousoperators-2022', 'https://bingtan.me/files/paper/TQ-AMP2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Modified inertial projection and contraction algorithms for solving variational inequality problems with non-Lipschitz continuous operators [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s13324-021-00638-6\"\n     onclick=\"log_download('tan-qin-modifiedinertialprojectionandcontractionalgorithmsforsolvingvariationalinequalityproblemswithnonlipschitzcontinuousoperators-2022', 'http://doi.org/10.1007/s13324-021-00638-6', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-qin-modifiedinertialprojectionandcontractionalgorithmsforsolvingvariationalinequalityproblemswithnonlipschitzcontinuousoperators-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-qin-modifiedinertialprojectionandcontractionalgorithmsforsolvingvariationalinequalityproblemswithnonlipschitzcontinuousoperators-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TQ_AMP22,\nauthor={Tan, Bing and Qin, Xiaolong},\ntitle={Modified inertial projection and contraction algorithms for solving variational inequality problems with non-Lipschitz continuous operators},\njournal={Analysis and Mathematical Physics},\nyear={2022},\nvolume={12},\nnumber={1},\ndoi={10.1007/s13324-021-00638-6},\npages={26},\nurl={https://bingtan.me/files/paper/TQ-AMP2022.pdf},\nabstract={In this paper, we present four modified inertial projection and contraction methods to solve the variational inequality problem with a pseudo-monotone and non-Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems of the proposed algorithms are established without the prior knowledge of the Lipschitz constant of the operator. Several numerical experiments and the applications to optimal control problems are provided to verify the advantages and efficiency of the proposed algorithms.},\nkeywords={Inertial method,  Projection and contraction method,  Pseudomonotone operator,  Subgradient extragradient method,  Non-Lipschitz operator,  Variational inequality problem},\nabbrev_source_title={Anal. Math. Phys.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we present four modified inertial projection and contraction methods to solve the variational inequality problem with a pseudo-monotone and non-Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems of the proposed algorithms are established without the prior knowledge of the Lipschitz constant of the operator. Several numerical experiments and the applications to optimal control problems are provided to verify the advantages and efficiency of the proposed algorithms.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-petruel-qin-yao-globalandlinearconvergenceofalternatedinertialsingleprojectionalgorithmsforpseudomonotonevariationalinequalities-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Petruşel, A.; Qin, X.;  and Yao, J. C.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Global and linear convergence of alternated inertial single projection algorithms for pseudo-monotone variational inequalities.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Fixed Point Theory</i>, 23(1): 391–426.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TPQY-FPT2022.pdf\"\n     onclick=\"log_download('tan-petruel-qin-yao-globalandlinearconvergenceofalternatedinertialsingleprojectionalgorithmsforpseudomonotonevariationalinequalities-2022', 'https://bingtan.me/files/paper/TPQY-FPT2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Global and linear convergence of alternated inertial single projection algorithms for pseudo-monotone variational inequalities [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.24193/fpt-ro.2022.1.25\"\n     onclick=\"log_download('tan-petruel-qin-yao-globalandlinearconvergenceofalternatedinertialsingleprojectionalgorithmsforpseudomonotonevariationalinequalities-2022', 'http://doi.org/10.24193/fpt-ro.2022.1.25', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-petruel-qin-yao-globalandlinearconvergenceofalternatedinertialsingleprojectionalgorithmsforpseudomonotonevariationalinequalities-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>2 downloads</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-petruel-qin-yao-globalandlinearconvergenceofalternatedinertialsingleprojectionalgorithmsforpseudomonotonevariationalinequalities-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TPQY_FPT22,\nauthor={Tan, Bing and Petruşel, Adrian and Qin, Xiaolong and Yao, Jen C.},\ntitle={Global and linear convergence of alternated inertial single projection algorithms for pseudo-monotone variational inequalities},\njournal={Fixed Point Theory},\nyear={2022},\nvolume={23},\nnumber={1},\npages={391--426},\ndoi={10.24193/fpt-ro.2022.1.25},\nurl={https://bingtan.me/files/paper/TPQY-FPT2022.pdf},\nabstract={In this paper, we investigate three new relaxed single projection methods with alternating inertial extrapolation steps and adaptive non-monotonic step sizes for solving pseudo-monotone variational inequalities in real Hilbert spaces. The proposed algorithms need to compute the projection on the feasible set only once in each iteration and they can work adaptively without the prior information of the Lipschitz constant of the mapping. The weak convergence theorems of the proposed iterative schemes are established under some appropriate conditions imposed on the parameters. These methods recover the Fejér monotonicity of the even subsequence with respect to the solution and obtain linear convergence rates. Finally, some numerical experiments and applications to optimal control problems are provided to demonstrate the advantages and efficiency of the proposed methods compared to some recent related ones.},\nkeywords={Adaptive stepsize,  Alternated inertial method,  Projection and contraction method,  Pseudomonotone operator,  Subgradient extragradient method,  Variational inequality problem},\nabbrev_source_title={Fixed Point Theory},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we investigate three new relaxed single projection methods with alternating inertial extrapolation steps and adaptive non-monotonic step sizes for solving pseudo-monotone variational inequalities in real Hilbert spaces. The proposed algorithms need to compute the projection on the feasible set only once in each iteration and they can work adaptively without the prior information of the Lipschitz constant of the mapping. The weak convergence theorems of the proposed iterative schemes are established under some appropriate conditions imposed on the parameters. These methods recover the Fejér monotonicity of the even subsequence with respect to the solution and obtain linear convergence rates. Finally, some numerical experiments and applications to optimal control problems are provided to demonstrate the advantages and efficiency of the proposed methods compared to some recent related ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-qin-adaptivemodifiedinertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalities-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Qin, X.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Adaptive modified inertial projection and contraction methods for pseudomonotone variational inequalities.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Applied and Numerical Optimization</i>, 4(2): 221–243.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TQ-JANO2022.pdf\"\n     onclick=\"log_download('tan-qin-adaptivemodifiedinertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalities-2022', 'https://bingtan.me/files/paper/TQ-JANO2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Adaptive modified inertial projection and contraction methods for pseudomonotone variational inequalities [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.23952/jano.4.2022.2.08\"\n     onclick=\"log_download('tan-qin-adaptivemodifiedinertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalities-2022', 'http://doi.org/10.23952/jano.4.2022.2.08', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-qin-adaptivemodifiedinertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalities-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-qin-adaptivemodifiedinertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalities-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TQ_JANO22,\nauthor={Tan, Bing and Qin, Xiaolong},\ntitle={Adaptive modified inertial projection and contraction methods for pseudomonotone variational inequalities},\njournal={Journal of Applied and Numerical Optimization},\nyear={2022},\nvolume={4},\nnumber={2},\npages={221--243},\ndoi={10.23952/jano.4.2022.2.08},\nurl={https://bingtan.me/files/paper/TQ-JANO2022.pdf},\nabstract={To handle pseudomonotone variational inequality problems in real Hilbert spaces, four modified inertial projection and contraction algorithms with non-monotonic step sizes are suggested in this paper. The proposed algorithms take advantage of a novel non-monotonic step size criteria, allowing them to work without previous knowledge of the Lipschitz constant of the mapping involved. Under certain situations, the strong convergence of the iterative sequences generated by the suggested algorithms is established. Finally, several numerical experiments are offered to validate the theoretical conclusions.},\nkeywords={Inertial method, Pseudomonotone operator, Projection and contraction method, Subgradient extragradient method, Variational inequality problem},\nabbrev_source_title={J. Appl. Numer. Optim.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  To handle pseudomonotone variational inequality problems in real Hilbert spaces, four modified inertial projection and contraction algorithms with non-monotonic step sizes are suggested in this paper. The proposed algorithms take advantage of a novel non-monotonic step size criteria, allowing them to work without previous knowledge of the Lipschitz constant of the mapping involved. Under certain situations, the strong convergence of the iterative sequences generated by the suggested algorithms is established. Finally, several numerical experiments are offered to validate the theoretical conclusions.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-qin-selfadaptiveviscositytypeinertialextragradientalgorithmsforsolvingvariationalinequalitieswithapplications-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Qin, X.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Self adaptive viscosity-type inertial extragradient algorithms for solving variational inequalities with applications.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Mathematical Modelling and Analysis</i>, 27(1): 41–58.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><span style=\"color: red\">(<s>ESI Highly Cited Paper</s>)</span></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TQ-MMA2022.pdf\"\n     onclick=\"log_download('tan-qin-selfadaptiveviscositytypeinertialextragradientalgorithmsforsolvingvariationalinequalitieswithapplications-2022', 'https://bingtan.me/files/paper/TQ-MMA2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Self adaptive viscosity-type inertial extragradient algorithms for solving variational inequalities with applications [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.3846/mma.2022.13846\"\n     onclick=\"log_download('tan-qin-selfadaptiveviscositytypeinertialextragradientalgorithmsforsolvingvariationalinequalitieswithapplications-2022', 'http://doi.org/10.3846/mma.2022.13846', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-qin-selfadaptiveviscositytypeinertialextragradientalgorithmsforsolvingvariationalinequalitieswithapplications-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-qin-selfadaptiveviscositytypeinertialextragradientalgorithmsforsolvingvariationalinequalitieswithapplications-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TQ_MMA22,\nauthor={Tan, Bing and Qin, Xiaolong},\ntitle={Self adaptive viscosity-type inertial extragradient algorithms for solving variational inequalities with applications},\njournal={Mathematical Modelling and Analysis},\nyear={2022},\nvolume={27},\nnumber={1},\npages={41--58},\ndoi={10.3846/mma.2022.13846},\nurl={https://bingtan.me/files/paper/TQ-MMA2022.pdf},\nabstract={In this paper, we introduce two new inertial extragradient algorithms with non-monotonic stepsizes for solving monotone and Lipschitz continuous variational inequality problems in real Hilbert spaces. Strong convergence theorems of the suggested iterative schemes are established without the prior knowledge of the Lipschitz constant of the mapping. Finally, some numerical examples are provided to illustrate the efficiency and advantages of the proposed algorithms and compare them with some related ones.},\nkeywords={Inertial method, Subgradient extragradient method,  Tseng&#x27;s extragradient method,  Optimal control problem,  Variational inequality problem,  Viscosity method},\nabbrev_source_title={Math. Model. Anal.},\nbibbase_note={&lt;span style=&quot;color: red&quot;&gt;(&lt;s&gt;ESI Highly Cited Paper&lt;/s&gt;)&lt;/span&gt;},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we introduce two new inertial extragradient algorithms with non-monotonic stepsizes for solving monotone and Lipschitz continuous variational inequality problems in real Hilbert spaces. Strong convergence theorems of the suggested iterative schemes are established without the prior knowledge of the Lipschitz constant of the mapping. Finally, some numerical examples are provided to illustrate the efficiency and advantages of the proposed algorithms and compare them with some related ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-liu-qin-strongconvergenceofinertialextragradientalgorithmsforsolvingvariationalinequalitiesandfixedpointproblems-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Liu, L.;  and Qin, X.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Strong convergence of inertial extragradient algorithms for solving variational inequalities and fixed point problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Fixed Point Theory</i>, 23(2): 707–728.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TLQ-FPT2022.pdf\"\n     onclick=\"log_download('tan-liu-qin-strongconvergenceofinertialextragradientalgorithmsforsolvingvariationalinequalitiesandfixedpointproblems-2022', 'https://bingtan.me/files/paper/TLQ-FPT2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Strong convergence of inertial extragradient algorithms for solving variational inequalities and fixed point problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.24193/fpt-ro.2022.2.17\"\n     onclick=\"log_download('tan-liu-qin-strongconvergenceofinertialextragradientalgorithmsforsolvingvariationalinequalitiesandfixedpointproblems-2022', 'http://doi.org/10.24193/fpt-ro.2022.2.17', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-liu-qin-strongconvergenceofinertialextragradientalgorithmsforsolvingvariationalinequalitiesandfixedpointproblems-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-liu-qin-strongconvergenceofinertialextragradientalgorithmsforsolvingvariationalinequalitiesandfixedpointproblems-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TLQ_FPT22,\nauthor={Tan, Bing and Liu, Liya and Qin, Xiaolong},\ntitle={Strong convergence of inertial extragradient algorithms for solving variational inequalities and fixed point problems},\njournal={Fixed Point Theory},\nyear={2022},\nvolume={23},\nnumber={2},\npages={707--728},\ndoi={10.24193/fpt-ro.2022.2.17},\nurl={https://bingtan.me/files/paper/TLQ-FPT2022.pdf},\nabstract={This paper investigates two inertial extragradient algorithms for seeking a common solution to a variational inequality problem involving a monotone and Lipschitz continuous mapping and a fixed point problem with a demicontractive mapping in real Hilbert spaces. Our algorithms need to calculate the projection on the feasible set only once in each iteration. Moreover, they can work well without the prior information of the Lipschitz constant of the operator and do not contain any linesearch process. Strong convergence theorems of the suggested algorithms are established under suitable conditions. Some experiments are presented to illustrate the numerical efficiency of the suggested algorithms and compare them with some existing ones.},\nkeywords={Variational inequality problem, Fixed point problem, Subgradient extragradient method, Tseng&#x27;s extragradient method, Inertial method, Demicontractive mapping},\nabbrev_source_title={Fixed Point Theory},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This paper investigates two inertial extragradient algorithms for seeking a common solution to a variational inequality problem involving a monotone and Lipschitz continuous mapping and a fixed point problem with a demicontractive mapping in real Hilbert spaces. Our algorithms need to calculate the projection on the feasible set only once in each iteration. Moreover, they can work well without the prior information of the Lipschitz constant of the operator and do not contain any linesearch process. Strong convergence theorems of the suggested algorithms are established under suitable conditions. Some experiments are presented to illustrate the numerical efficiency of the suggested algorithms and compare them with some existing ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"fan-qin-tan-tsengsextragradientalgorithmforpseudomonotonevariationalinequalitiesonhadamardmanifolds-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Fan, J.; Qin, X.;  and <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Tseng's extragradient algorithm for pseudomonotone variational inequalities on Hadamard manifolds.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Applicable Analysis</i>, 101(6): 2372–2385.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/FQT-AA2022.pdf\"\n     onclick=\"log_download('fan-qin-tan-tsengsextragradientalgorithmforpseudomonotonevariationalinequalitiesonhadamardmanifolds-2022', 'https://bingtan.me/files/paper/FQT-AA2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Tseng&#x27;s extragradient algorithm for pseudomonotone variational inequalities on Hadamard manifolds [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1080/00036811.2020.1807012\"\n     onclick=\"log_download('fan-qin-tan-tsengsextragradientalgorithmforpseudomonotonevariationalinequalitiesonhadamardmanifolds-2022', 'http://doi.org/10.1080/00036811.2020.1807012', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/fan-qin-tan-tsengsextragradientalgorithmforpseudomonotonevariationalinequalitiesonhadamardmanifolds-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('fan-qin-tan-tsengsextragradientalgorithmforpseudomonotonevariationalinequalitiesonhadamardmanifolds-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{FQT_AA22,\nauthor={Fan, Jingjing and Qin, Xiaolong and Tan, Bing},\ntitle={Tseng&#x27;s extragradient algorithm for pseudomonotone variational inequalities on {H}adamard manifolds},\njournal={Applicable Analysis},\nyear={2022},\nvolume={101},\nnumber={6},\npages={2372--2385},\ndoi={10.1080/00036811.2020.1807012},\nurl={https://bingtan.me/files/paper/FQT-AA2022.pdf},\nabstract={In this paper, we investigate the Tseng&#x27;s extragradient algorithm for non-Lipschitzian variational inequalities with pseudomonotone vector fields on Hadamard manifolds. The convergence analysis of the proposed algorithm is discussed under mild assumptions. Two experiments are provided to illustrate the asymptotical behavior of the algorithm. The results presented in this paper generalize some known results presented in the literature.},\nkeywords={Extragradient method,  Hadamard manifolds,  Non-Lipschitz operator,  Pseudomonotone vector field,  Variational inequality problem},\nabbrev_source_title={Appl. Anal.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we investigate the Tseng's extragradient algorithm for non-Lipschitzian variational inequalities with pseudomonotone vector fields on Hadamard manifolds. The convergence analysis of the proposed algorithm is discussed under mild assumptions. Two experiments are provided to illustrate the asymptotical behavior of the algorithm. The results presented in this paper generalize some known results presented in the literature.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-qin-yao-strongconvergenceofselfadaptiveinertialalgorithmsforsolvingsplitvariationalinclusionproblemswithapplications-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Qin, X.;  and Yao, J. C.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Strong convergence of self-adaptive inertial algorithms for solving split variational inclusion problems with applications.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Scientific Computing</i>, 87(1): 20.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><span style=\"color: red\">(ESI Highly Cited Paper)</span></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TQY-JSC2021.pdf\"\n     onclick=\"log_download('tan-qin-yao-strongconvergenceofselfadaptiveinertialalgorithmsforsolvingsplitvariationalinclusionproblemswithapplications-2021', 'https://bingtan.me/files/paper/TQY-JSC2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Strong convergence of self-adaptive inertial algorithms for solving split variational inclusion problems with applications [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s10915-021-01428-9\"\n     onclick=\"log_download('tan-qin-yao-strongconvergenceofselfadaptiveinertialalgorithmsforsolvingsplitvariationalinclusionproblemswithapplications-2021', 'http://doi.org/10.1007/s10915-021-01428-9', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-qin-yao-strongconvergenceofselfadaptiveinertialalgorithmsforsolvingsplitvariationalinclusionproblemswithapplications-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-qin-yao-strongconvergenceofselfadaptiveinertialalgorithmsforsolvingsplitvariationalinclusionproblemswithapplications-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TQY_JSC21,\nauthor={Tan, Bing and Qin, Xiaolong and Yao, Jen C.},\ntitle={Strong convergence of self-adaptive inertial algorithms for solving split variational inclusion problems with applications},\njournal={Journal of Scientific Computing},\nyear={2021},\nvolume={87},\nnumber={1},\ndoi={10.1007/s10915-021-01428-9},\npages={20},\nurl={https://bingtan.me/files/paper/TQY-JSC2021.pdf},\nabstract={In this paper, four self-adaptive iterative algorithms with inertial effects are introduced to solve a split variational inclusion problem in real Hilbert spaces. One of the advantages of the suggested algorithms is that they can work without knowing the prior information of the operator norm. Strong convergence theorems of these algorithms are established under mild and standard assumptions. As applications, the split feasibility problem and the split minimization problem in real Hilbert spaces are studied. Finally, several preliminary numerical experiments as well as an example in the field of compressed sensing are proposed to support the advantages and efficiency of the suggested methods over some existing ones.},\nkeywords={Inertial method,  Mann method,  Signal processing problem,  Split variational inclusion problem,  Strong convergence,  Viscosity method},\nabbrev_source_title={J. Sci. Comput.},\nbibbase_note={&lt;span style=&quot;color: red&quot;&gt;(ESI Highly Cited Paper)&lt;/span&gt;},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, four self-adaptive iterative algorithms with inertial effects are introduced to solve a split variational inclusion problem in real Hilbert spaces. One of the advantages of the suggested algorithms is that they can work without knowing the prior information of the operator norm. Strong convergence theorems of these algorithms are established under mild and standard assumptions. As applications, the split feasibility problem and the split minimization problem in real Hilbert spaces are studied. Finally, several preliminary numerical experiments as well as an example in the field of compressed sensing are proposed to support the advantages and efficiency of the suggested methods over some existing ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-qin-yao-twomodifiedinertialprojectionalgorithmsforbilevelpseudomonotonevariationalinequalitieswithapplicationstooptimalcontrolproblems-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Qin, X.;  and Yao, J. C.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Two modified inertial projection algorithms for bilevel pseudomonotone variational inequalities with applications to optimal control problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Numerical Algorithms</i>, 88(4): 1757–1786.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TQY-NUMA2021.pdf\"\n     onclick=\"log_download('tan-qin-yao-twomodifiedinertialprojectionalgorithmsforbilevelpseudomonotonevariationalinequalitieswithapplicationstooptimalcontrolproblems-2021', 'https://bingtan.me/files/paper/TQY-NUMA2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Two modified inertial projection algorithms for bilevel pseudomonotone variational inequalities with applications to optimal control problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s11075-021-01093-x\"\n     onclick=\"log_download('tan-qin-yao-twomodifiedinertialprojectionalgorithmsforbilevelpseudomonotonevariationalinequalitieswithapplicationstooptimalcontrolproblems-2021', 'http://doi.org/10.1007/s11075-021-01093-x', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-qin-yao-twomodifiedinertialprojectionalgorithmsforbilevelpseudomonotonevariationalinequalitieswithapplicationstooptimalcontrolproblems-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-qin-yao-twomodifiedinertialprojectionalgorithmsforbilevelpseudomonotonevariationalinequalitieswithapplicationstooptimalcontrolproblems-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TQY_NUMA21,\nauthor={Tan, Bing and Qin, Xiaolong and Yao, Jen C.},\ntitle={Two modified inertial projection algorithms for bilevel pseudomonotone variational inequalities with applications to optimal control problems},\njournal={Numerical Algorithms},\nyear={2021},\nvolume={88},\nnumber={4},\npages={1757--1786},\ndoi={10.1007/s11075-021-01093-x},\nurl={https://bingtan.me/files/paper/TQY-NUMA2021.pdf},\nabstract={In this paper, we investigate two new algorithms for solving bilevel pseudomonotone variational inequality problems in real Hilbert spaces. The advantages of our algorithms are that they only need to calculate one projection on the feasible set in each iteration, and do not require the prior information of the Lipschitz constant of the cost operator. Furthermore, two new algorithms are derived to solve variational inequality problems. We establish the strong convergence of the proposed algorithms under some suitable conditions imposed on parameters. Finally, several numerical results and applications in optimal control problems are reported to illustrate the efficiency and advantages of the proposed algorithms.},\nkeywords={Bilevel variational inequality problem,  Hybrid steepest descent method,  Inertial extragradient method,  Projection and contraction method,  Pseudomonotone operator},\nabbrev_source_title={Numer. Algorithms},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we investigate two new algorithms for solving bilevel pseudomonotone variational inequality problems in real Hilbert spaces. The advantages of our algorithms are that they only need to calculate one projection on the feasible set in each iteration, and do not require the prior information of the Lipschitz constant of the cost operator. Furthermore, two new algorithms are derived to solve variational inequality problems. We establish the strong convergence of the proposed algorithms under some suitable conditions imposed on parameters. Finally, several numerical results and applications in optimal control problems are reported to illustrate the efficiency and advantages of the proposed algorithms.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-liu-qin-selfadaptiveinertialextragradientalgorithmsforsolvingbilevelpseudomonotonevariationalinequalityproblems-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Liu, L.;  and Qin, X.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Self adaptive inertial extragradient algorithms for solving bilevel pseudomonotone variational inequality problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Japan Journal of Industrial and Applied Mathematics</i>, 38(2): 519-543.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><span style=\"color: red\">(<s>ESI Highly Cited Paper</s>)</span></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TLQ-JIAM2021.pdf\"\n     onclick=\"log_download('tan-liu-qin-selfadaptiveinertialextragradientalgorithmsforsolvingbilevelpseudomonotonevariationalinequalityproblems-2021', 'https://bingtan.me/files/paper/TLQ-JIAM2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Self adaptive inertial extragradient algorithms for solving bilevel pseudomonotone variational inequality problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s13160-020-00450-y\"\n     onclick=\"log_download('tan-liu-qin-selfadaptiveinertialextragradientalgorithmsforsolvingbilevelpseudomonotonevariationalinequalityproblems-2021', 'http://doi.org/10.1007/s13160-020-00450-y', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-liu-qin-selfadaptiveinertialextragradientalgorithmsforsolvingbilevelpseudomonotonevariationalinequalityproblems-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-liu-qin-selfadaptiveinertialextragradientalgorithmsforsolvingbilevelpseudomonotonevariationalinequalityproblems-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TLQ_JIAM21,\nauthor={Tan, Bing and Liu, Liya and Qin, Xiaolong},\ntitle={Self adaptive inertial extragradient algorithms for solving bilevel pseudomonotone variational inequality problems},\njournal={Japan Journal of Industrial and Applied Mathematics},\nyear={2021},\nvolume={38},\nnumber={2},\npages={519-543},\ndoi={10.1007/s13160-020-00450-y},\nurl={https://bingtan.me/files/paper/TLQ-JIAM2021.pdf},\nabstract={We introduce two inertial extragradient algorithms for solving a bilevel pseudomonotone variational inequality problem in real Hilbert spaces. The advantages of the proposed algorithms are that they can work without the prior knowledge of the Lipschitz constant of the involving operator and only one projection onto the feasible set is required. Strong convergence theorems of the suggested algorithms are obtained under suitable conditions. Finally, some numerical examples are provided to show the efficiency of the proposed algorithms.},\nkeywords={Bilevel variational inequality problem,  Inertial method, Subgradient extragradient method,  Tseng&#x27;s extragradient method,  Pseudomonotone operator,  Hybrid steepest descent method},\nabbrev_source_title={Jpn J. Ind. Appl. Math.},\nbibbase_note={&lt;span style=&quot;color: red&quot;&gt;(&lt;s&gt;ESI Highly Cited Paper&lt;/s&gt;)&lt;/span&gt;},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We introduce two inertial extragradient algorithms for solving a bilevel pseudomonotone variational inequality problem in real Hilbert spaces. The advantages of the proposed algorithms are that they can work without the prior knowledge of the Lipschitz constant of the involving operator and only one projection onto the feasible set is required. Strong convergence theorems of the suggested algorithms are obtained under suitable conditions. Finally, some numerical examples are provided to show the efficiency of the proposed algorithms.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-fan-qin-inertialextragradientalgorithmswithnonmonotonicstepsizesforsolvingvariationalinequalitiesandfixedpointproblems-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Fan, J.;  and Qin, X.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Inertial extragradient algorithms with non-monotonic step sizes for solving variational inequalities and fixed point problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Advances in Operator Theory</i>, 6(4): 61.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TFQ-AIOT2021.pdf\"\n     onclick=\"log_download('tan-fan-qin-inertialextragradientalgorithmswithnonmonotonicstepsizesforsolvingvariationalinequalitiesandfixedpointproblems-2021', 'https://bingtan.me/files/paper/TFQ-AIOT2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Inertial extragradient algorithms with non-monotonic step sizes for solving variational inequalities and fixed point problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s43036-021-00155-0\"\n     onclick=\"log_download('tan-fan-qin-inertialextragradientalgorithmswithnonmonotonicstepsizesforsolvingvariationalinequalitiesandfixedpointproblems-2021', 'http://doi.org/10.1007/s43036-021-00155-0', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-fan-qin-inertialextragradientalgorithmswithnonmonotonicstepsizesforsolvingvariationalinequalitiesandfixedpointproblems-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-fan-qin-inertialextragradientalgorithmswithnonmonotonicstepsizesforsolvingvariationalinequalitiesandfixedpointproblems-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TFQ_AIOT21,\nauthor={Tan, Bing and Fan, Jingjing and Qin, Xiaolong},\ntitle={Inertial extragradient algorithms with non-monotonic step sizes for solving variational inequalities and fixed point problems},\njournal={Advances in Operator Theory},\nyear={2021},\nvolume={6},\nnumber={4},\ndoi={10.1007/s43036-021-00155-0},\npages={61},\nurl={https://bingtan.me/files/paper/TFQ-AIOT2021.pdf},\nabstract={In this paper, we introduce four inertial extragradient algorithms with non-monotonic step sizes to find the solution of the convex feasibility problem, which consists of a monotone variational inequality problem and a fixed point problem with a demicontractive mapping. Strong convergence theorems of the suggested algorithms are established under some standard conditions. Finally, we implement some computational tests to show the efficiency and advantages of the proposed algorithms and compare them with some existing ones.},\nkeywords={Fixed point problem,  Inertial method,  Strong convergence,  Subgradient extragradient method,  Tseng&#x27;s extragradient method,  Variational inequality problem},\nabbrev_source_title={Adv. Oper. Theory},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we introduce four inertial extragradient algorithms with non-monotonic step sizes to find the solution of the convex feasibility problem, which consists of a monotone variational inequality problem and a fixed point problem with a demicontractive mapping. Strong convergence theorems of the suggested algorithms are established under some standard conditions. Finally, we implement some computational tests to show the efficiency and advantages of the proposed algorithms and compare them with some existing ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-li-qin-selfadaptiveinertialsingleprojectionmethodsforvariationalinequalitiesinvolvingnonlipschitzandlipschitzoperatorswiththeirapplicationstooptimalcontrolproblems-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Li, S.;  and Qin, X.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Self-adaptive inertial single projection methods for variational inequalities involving non-Lipschitz and Lipschitz operators with their applications to optimal control problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Applied Numerical Mathematics</i>, 170: 219–241.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TLQ-ANM2021.pdf\"\n     onclick=\"log_download('tan-li-qin-selfadaptiveinertialsingleprojectionmethodsforvariationalinequalitiesinvolvingnonlipschitzandlipschitzoperatorswiththeirapplicationstooptimalcontrolproblems-2021', 'https://bingtan.me/files/paper/TLQ-ANM2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Self-adaptive inertial single projection methods for variational inequalities involving non-Lipschitz and Lipschitz operators with their applications to optimal control problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1016/j.apnum.2021.07.022\"\n     onclick=\"log_download('tan-li-qin-selfadaptiveinertialsingleprojectionmethodsforvariationalinequalitiesinvolvingnonlipschitzandlipschitzoperatorswiththeirapplicationstooptimalcontrolproblems-2021', 'http://doi.org/10.1016/j.apnum.2021.07.022', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-li-qin-selfadaptiveinertialsingleprojectionmethodsforvariationalinequalitiesinvolvingnonlipschitzandlipschitzoperatorswiththeirapplicationstooptimalcontrolproblems-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-li-qin-selfadaptiveinertialsingleprojectionmethodsforvariationalinequalitiesinvolvingnonlipschitzandlipschitzoperatorswiththeirapplicationstooptimalcontrolproblems-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TLQ_ANM21,\nauthor={Tan, Bing and Li, Songxiao and Qin, Xiaolong},\ntitle={Self-adaptive inertial single projection methods for variational inequalities involving non-Lipschitz and Lipschitz operators with their applications to optimal control problems},\njournal={Applied Numerical Mathematics},\nyear={2021},\nvolume={170},\npages={219--241},\ndoi={10.1016/j.apnum.2021.07.022},\nurl={https://bingtan.me/files/paper/TLQ-ANM2021.pdf},\nabstract={In this paper, four accelerated subgradient extragradient methods are proposed to solve the variational inequality problem with a pseudo-monotone operator in real Hilbert spaces. These iterative schemes employ two new adaptive stepsize strategies that are significant when the Lipschitz constant of the mapping involved is unknown. Strong convergence theorems for the proposed algorithms are established under the condition that the operators are Lipschitz continuous and non-Lipschitz continuous. Numerical experiments on finite- and infinite-dimensional spaces and applications in optimal control problems are reported to demonstrate the advantages and efficiency of the proposed algorithms over some existing results.},\nkeywords={Inertial method, Subgradient extragradient method,  Optimal control problem,  Pseudomonotone operator,  Non-Lipschitz operator,  Variational inequality problem},\nabbrev_source_title={Appl Numer Math},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, four accelerated subgradient extragradient methods are proposed to solve the variational inequality problem with a pseudo-monotone operator in real Hilbert spaces. These iterative schemes employ two new adaptive stepsize strategies that are significant when the Lipschitz constant of the mapping involved is unknown. Strong convergence theorems for the proposed algorithms are established under the condition that the operators are Lipschitz continuous and non-Lipschitz continuous. Numerical experiments on finite- and infinite-dimensional spaces and applications in optimal control problems are reported to demonstrate the advantages and efficiency of the proposed algorithms over some existing results.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-li-qin-anacceleratedextragradientalgorithmforbilevelpseudomonotonevariationalinequalityproblemswithapplicationtooptimalcontrolproblems-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Li, S.;  and Qin, X.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  An accelerated extragradient algorithm for bilevel pseudomonotone variational inequality problems with application to optimal control problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas</i>, 115(4): 174.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TLQ-RACSAM2021.pdf\"\n     onclick=\"log_download('tan-li-qin-anacceleratedextragradientalgorithmforbilevelpseudomonotonevariationalinequalityproblemswithapplicationtooptimalcontrolproblems-2021', 'https://bingtan.me/files/paper/TLQ-RACSAM2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"An accelerated extragradient algorithm for bilevel pseudomonotone variational inequality problems with application to optimal control problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s13398-021-01116-1\"\n     onclick=\"log_download('tan-li-qin-anacceleratedextragradientalgorithmforbilevelpseudomonotonevariationalinequalityproblemswithapplicationtooptimalcontrolproblems-2021', 'http://doi.org/10.1007/s13398-021-01116-1', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-li-qin-anacceleratedextragradientalgorithmforbilevelpseudomonotonevariationalinequalityproblemswithapplicationtooptimalcontrolproblems-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-li-qin-anacceleratedextragradientalgorithmforbilevelpseudomonotonevariationalinequalityproblemswithapplicationtooptimalcontrolproblems-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TLQ_RCSM21,\nauthor={Tan, Bing and Li, Songxiao and Qin, Xiaolong},\ntitle={An accelerated extragradient algorithm for bilevel pseudomonotone variational inequality problems with application to optimal control problems},\njournal={Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas},\nyear={2021},\nvolume={115},\nnumber={4},\ndoi={10.1007/s13398-021-01116-1},\npages={174},\nurl={https://bingtan.me/files/paper/TLQ-RACSAM2021.pdf},\nabstract={In this paper, an inertial extragradient algorithm with a new non-monotonic stepsize is proposed to solve the bilevel pseudomonotone variational inequality problem in real Hilbert spaces. The advantages of the suggested iterative algorithm are that only one projection onto the feasible set needs to be performed in each iteration and the prior knowledge of the Lipschitz constant of the mapping involved does not require to be known. The strong convergence theorem of the suggested algorithm is established under some suitable conditions. Numerical experiments are reported to illustrate the advantages and efficiency of the presented algorithm over the existing related ones.},\nkeywords={Bilevel variational inequality problem,  Hybrid steepest descent method,  Inertial extragradient method,  Projection and contraction method,  Pseudomonotone operator},\nabbrev_source_title={Rev. R. Acad. Cienc. Exactas F{\\&#x27; i}s. Nat. Ser. A Mat. RACSAM},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, an inertial extragradient algorithm with a new non-monotonic stepsize is proposed to solve the bilevel pseudomonotone variational inequality problem in real Hilbert spaces. The advantages of the suggested iterative algorithm are that only one projection onto the feasible set needs to be performed in each iteration and the prior knowledge of the Lipschitz constant of the mapping involved does not require to be known. The strong convergence theorem of the suggested algorithm is established under some suitable conditions. Numerical experiments are reported to illustrate the advantages and efficiency of the presented algorithm over the existing related ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-li-qin-onmodifiedsubgradientextragradientmethodsforpseudomonotonevariationalinequalityproblemswithapplications-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Li, S.;  and Qin, X.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  On modified subgradient extragradient methods for pseudomonotone variational inequality problems with applications.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Computational and Applied Mathematics</i>, 40(7): 253.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TLQ-COAM2021.pdf\"\n     onclick=\"log_download('tan-li-qin-onmodifiedsubgradientextragradientmethodsforpseudomonotonevariationalinequalityproblemswithapplications-2021', 'https://bingtan.me/files/paper/TLQ-COAM2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"On modified subgradient extragradient methods for pseudomonotone variational inequality problems with applications [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s40314-021-01642-z\"\n     onclick=\"log_download('tan-li-qin-onmodifiedsubgradientextragradientmethodsforpseudomonotonevariationalinequalityproblemswithapplications-2021', 'http://doi.org/10.1007/s40314-021-01642-z', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-li-qin-onmodifiedsubgradientextragradientmethodsforpseudomonotonevariationalinequalityproblemswithapplications-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-li-qin-onmodifiedsubgradientextragradientmethodsforpseudomonotonevariationalinequalityproblemswithapplications-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TLQ_COAM21,\nauthor={Tan, Bing and Li, Songxiao and Qin, Xiaolong},\ntitle={On modified subgradient extragradient methods for pseudomonotone variational inequality problems with applications},\njournal={Computational and Applied Mathematics},\nyear={2021},\nvolume={40},\nnumber={7},\ndoi={10.1007/s40314-021-01642-z},\npages={253},\nurl={https://bingtan.me/files/paper/TLQ-COAM2021.pdf},\nabstract={This paper presents several modified subgradient extragradient methods with inertial effects to approximate solutions of variational inequality problems in real Hilbert spaces. The operators involved are either pseudomonotone Lipschitz continuous or pseudomonotone non-Lipschitz continuous. The advantage of the suggested algorithms is that they can work adaptively without the prior information of the Lipschitz constant of the mapping involved. Strong convergence theorems of the proposed algorithms are established under some suitable conditions. Finally, some numerical experiments are given to verify the advantages and efficiency of the proposed iterative algorithms with respect to previously known ones.},\nkeywords={Extragradient method,  Non-Lipschitz operator,  Optimal control problem,  Pseudomonotone operator,  Variational inequality problem},\nabbrev_source_title={Comput. Appl. Math.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This paper presents several modified subgradient extragradient methods with inertial effects to approximate solutions of variational inequality problems in real Hilbert spaces. The operators involved are either pseudomonotone Lipschitz continuous or pseudomonotone non-Lipschitz continuous. The advantage of the suggested algorithms is that they can work adaptively without the prior information of the Lipschitz constant of the mapping involved. Strong convergence theorems of the proposed algorithms are established under some suitable conditions. Finally, some numerical experiments are given to verify the advantages and efficiency of the proposed iterative algorithms with respect to previously known ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"fan-qin-tan-convergenceofaninertialshadowdouglasrachfordsplittingalgorithmformonotoneinclusions-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Fan, J.; Qin, X.;  and <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Convergence of an inertial shadow Douglas-Rachford splitting algorithm for monotone inclusions.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Numerical Functional Analysis and Optimization</i>, 42(14): 1627–1644.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/FQT-NFAO2021.pdf\"\n     onclick=\"log_download('fan-qin-tan-convergenceofaninertialshadowdouglasrachfordsplittingalgorithmformonotoneinclusions-2021', 'https://bingtan.me/files/paper/FQT-NFAO2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Convergence of an inertial shadow Douglas-Rachford splitting algorithm for monotone inclusions [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1080/01630563.2021.2001749\"\n     onclick=\"log_download('fan-qin-tan-convergenceofaninertialshadowdouglasrachfordsplittingalgorithmformonotoneinclusions-2021', 'http://doi.org/10.1080/01630563.2021.2001749', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/fan-qin-tan-convergenceofaninertialshadowdouglasrachfordsplittingalgorithmformonotoneinclusions-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('fan-qin-tan-convergenceofaninertialshadowdouglasrachfordsplittingalgorithmformonotoneinclusions-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{FQT_NFAO21,\nauthor={Fan, Jingjing and Qin, Xiaolong and Tan, Bing},\ntitle={Convergence of an inertial shadow {D}ouglas-{R}achford splitting algorithm for monotone inclusions},\njournal={Numerical Functional Analysis and Optimization},\nyear={2021},\nvolume={42},\nnumber={14},\npages={1627--1644},\ndoi={10.1080/01630563.2021.2001749},\nurl={https://bingtan.me/files/paper/FQT-NFAO2021.pdf},\nabstract={An inertial shadow Douglas-Rachford splitting algorithm for finding zeros of the sum of monotone operators is proposed in Hilbert spaces. Moreover, a three-operator splitting algorithm for solving a class of monotone inclusion problems is also concerned. The weak convergence of the algorithms is investigated under mild assumptions. Some numerical experiments are implemented to illustrate our main convergence results.},\nkeywords={Inertial method,  Monotone inclusion,  Shadow Douglas-Rachford splitting algorithm,  Three-operator splitting},\nabbrev_source_title={Numer. Funct. Anal. Optim.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  An inertial shadow Douglas-Rachford splitting algorithm for finding zeros of the sum of monotone operators is proposed in Hilbert spaces. Moreover, a three-operator splitting algorithm for solving a class of monotone inclusion problems is also concerned. The weak convergence of the algorithms is investigated under mild assumptions. Some numerical experiments are implemented to illustrate our main convergence results.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-zhou-qin-acceleratedprojectionbasedforwardbackwardsplittingalgorithmsformonotoneinclusionproblems-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Zhou, Z.;  and Qin, X.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Accelerated projection-based forward-backward splitting algorithms for monotone inclusion problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Applied Analysis and Computation</i>, 10(5): 2184–2197.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TZQ-JAAC2020.pdf\"\n     onclick=\"log_download('tan-zhou-qin-acceleratedprojectionbasedforwardbackwardsplittingalgorithmsformonotoneinclusionproblems-2020', 'https://bingtan.me/files/paper/TZQ-JAAC2020.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Accelerated projection-based forward-backward splitting algorithms for monotone inclusion problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.11948/20190363\"\n     onclick=\"log_download('tan-zhou-qin-acceleratedprojectionbasedforwardbackwardsplittingalgorithmsformonotoneinclusionproblems-2020', 'http://doi.org/10.11948/20190363', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-zhou-qin-acceleratedprojectionbasedforwardbackwardsplittingalgorithmsformonotoneinclusionproblems-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-zhou-qin-acceleratedprojectionbasedforwardbackwardsplittingalgorithmsformonotoneinclusionproblems-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TZQ_JAAC20,\nauthor={Tan, Bing and Zhou, Zheng and Qin, Xiaolong},\ntitle={Accelerated projection-based forward-backward splitting algorithms for monotone inclusion problems},\njournal={Journal of Applied Analysis and Computation},\nyear={2020},\nvolume={10},\nnumber={5},\npages={2184--2197},\ndoi={10.11948/20190363},\nurl={https://bingtan.me/files/paper/TZQ-JAAC2020.pdf},\nabstract={In this paper, based on inertial and Tseng&#x27;s ideas, we propose two projection-based algorithms to solve a monotone inclusion problem in infinite dimensional Hilbert spaces. Solution theorems of strong convergence are obtained under the certain conditions. Some numerical experiments are presented to illustrate that our algorithms are efficient than the existing results.},\nkeywords={Forward-backward splitting algorithm,  Inclusion problem,  Monotone operator,  Strong convergence},\nabbrev_source_title={J. Appl. Anal. Comput.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, based on inertial and Tseng's ideas, we propose two projection-based algorithms to solve a monotone inclusion problem in infinite dimensional Hilbert spaces. Solution theorems of strong convergence are obtained under the certain conditions. Some numerical experiments are presented to illustrate that our algorithms are efficient than the existing results.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_Shang__M_\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_Shang__M_')\"\n      onkeypress=\"toggleGroup('group_Shang__M_')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>Shang, M.</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"luo-shang-tan-ageneralinertialviscositytypemethodfornonexpansivemappingsanditsapplicationsinsignalprocessing-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Luo, Y.; Shang, M.;  and <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  A general inertial viscosity type method for nonexpansive mappings and its applications in signal processing.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Mathematics</i>, 8(2): 288.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/LST-Math2020.pdf\"\n     onclick=\"log_download('luo-shang-tan-ageneralinertialviscositytypemethodfornonexpansivemappingsanditsapplicationsinsignalprocessing-2020', 'https://bingtan.me/files/paper/LST-Math2020.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"A general inertial viscosity type method for nonexpansive mappings and its applications in signal processing [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.3390/math8020288\"\n     onclick=\"log_download('luo-shang-tan-ageneralinertialviscositytypemethodfornonexpansivemappingsanditsapplicationsinsignalprocessing-2020', 'http://doi.org/10.3390/math8020288', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/luo-shang-tan-ageneralinertialviscositytypemethodfornonexpansivemappingsanditsapplicationsinsignalprocessing-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('luo-shang-tan-ageneralinertialviscositytypemethodfornonexpansivemappingsanditsapplicationsinsignalprocessing-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{LST_MATH20,\nauthor={Luo, Yinglin and Shang, Meijuan and Tan, Bing},\ntitle={A general inertial viscosity type method for nonexpansive mappings and its applications in signal processing},\njournal={Mathematics},\nyear={2020},\nvolume={8},\nnumber={2},\ndoi={10.3390/math8020288},\npages={288},\nurl={https://bingtan.me/files/paper/LST-Math2020.pdf},\nabstract={In this paper, we propose viscosity algorithms with two different inertia parameters for solving fixed points of nonexpansive and strictly pseudocontractive mappings. Strong convergence theorems are obtained in Hilbert spaces and the applications to the signal processing are considered. Moreover, some numerical experiments of proposed algorithms and comparisons with existing algorithms are given to the demonstration of the efficiency of the proposed algorithms. The numerical results show that our algorithms are superior to some related algorithms.},\nkeywords={Inclusion problem,  Nonexpansive mapping,  Signal processing problem,  Strict pseudo-contraction,  Variational inequality problem},\nabbrev_source_title={Mathematics},\n}\n\n\n\n\n\n\n\n\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we propose viscosity algorithms with two different inertia parameters for solving fixed points of nonexpansive and strictly pseudocontractive mappings. Strong convergence theorems are obtained in Hilbert spaces and the applications to the signal processing are considered. Moreover, some numerical experiments of proposed algorithms and comparisons with existing algorithms are given to the demonstration of the efficiency of the proposed algorithms. The numerical results show that our algorithms are superior to some related algorithms.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_Sunthrayuth__P_\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_Sunthrayuth__P_')\"\n      onkeypress=\"toggleGroup('group_Sunthrayuth__P_')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>Sunthrayuth, P.</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"tan-sunthrayuth-cholamjiak-cho-modifiedinertialextragradientmethodsforfindingminimumnormsolutionofthevariationalinequalityproblemwithapplicationstooptimalcontrolproblem-2023\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Sunthrayuth, P.; Cholamjiak, P.;  and Cho, Y. J.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Modified inertial extragradient methods for finding minimum-norm solution of the variational inequality problem with applications to optimal control problem.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>International Journal of Computer Mathematics</i>, 100(3): 525–545.  2023.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TSCC-IJCM23.pdf\"\n     onclick=\"log_download('tan-sunthrayuth-cholamjiak-cho-modifiedinertialextragradientmethodsforfindingminimumnormsolutionofthevariationalinequalityproblemwithapplicationstooptimalcontrolproblem-2023', 'https://bingtan.me/files/paper/TSCC-IJCM23.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Modified inertial extragradient methods for finding minimum-norm solution of the variational inequality problem with applications to optimal control problem [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1080/00207160.2022.2137672\"\n     onclick=\"log_download('tan-sunthrayuth-cholamjiak-cho-modifiedinertialextragradientmethodsforfindingminimumnormsolutionofthevariationalinequalityproblemwithapplicationstooptimalcontrolproblem-2023', 'http://doi.org/10.1080/00207160.2022.2137672', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-sunthrayuth-cholamjiak-cho-modifiedinertialextragradientmethodsforfindingminimumnormsolutionofthevariationalinequalityproblemwithapplicationstooptimalcontrolproblem-2023\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-sunthrayuth-cholamjiak-cho-modifiedinertialextragradientmethodsforfindingminimumnormsolutionofthevariationalinequalityproblemwithapplicationstooptimalcontrolproblem-2023')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TSCC_IJCM23,\nauthor={Tan, Bing and Sunthrayuth, Pongsakorn and Cholamjiak, Prasit and  Cho, Yeol J.},\ntitle={Modified inertial extragradient methods for finding minimum-norm solution of the variational inequality problem with applications to optimal control problem},\njournal={International Journal of Computer Mathematics},\nyear={2023},\nvolume={100},\nnumber={3},\npages={525--545},\ndoi={10.1080/00207160.2022.2137672},\nurl={https://bingtan.me/files/paper/TSCC-IJCM23.pdf},\nabstract={In order to discover the minimum-norm solution of the pseudomonotone variational inequality problem in a real Hilbert space, we provide two variants of the inertial extragradient approach with a novel generalized adaptive step size. Two of the suggested algorithms make use of the projection and contraction methods. We demonstrate several strong convergence findings without requiring the prior knowledge of the Lipschitz constant of the mapping. Finally, we give a number of numerical examples that highlight the benefits and effectiveness of the suggested algorithms and how they may be used to solve the optimal control problem.},\nkeywords={Variational inequality problem, Optimal control problem, Inertial method, Projection and contraction method},\nabbrev_source_title={Int. J. Comput. Math.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In order to discover the minimum-norm solution of the pseudomonotone variational inequality problem in a real Hilbert space, we provide two variants of the inertial extragradient approach with a novel generalized adaptive step size. Two of the suggested algorithms make use of the projection and contraction methods. We demonstrate several strong convergence findings without requiring the prior knowledge of the Lipschitz constant of the mapping. Finally, we give a number of numerical examples that highlight the benefits and effectiveness of the suggested algorithms and how they may be used to solve the optimal control problem.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_Tan__B_\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_Tan__B_')\"\n      onkeypress=\"toggleGroup('group_Tan__B_')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>Tan, B.</span>\n      <span class=\"bibbase_group_count\">\n        \n        (58)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"tan-qin-wang-alternatedinertialalgorithmsforsplitfeasibilityproblems-2024\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Qin, X.;  and Wang, X.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Alternated inertial algorithms for split feasibility problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Numerical Algorithms</i>, 95(2): 773–812.  2024.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TQW-NUMA2024.pdf\"\n     onclick=\"log_download('tan-qin-wang-alternatedinertialalgorithmsforsplitfeasibilityproblems-2024', 'https://bingtan.me/files/paper/TQW-NUMA2024.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Alternated inertial algorithms for split feasibility problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s11075-023-01589-8\"\n     onclick=\"log_download('tan-qin-wang-alternatedinertialalgorithmsforsplitfeasibilityproblems-2024', 'http://doi.org/10.1007/s11075-023-01589-8', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-qin-wang-alternatedinertialalgorithmsforsplitfeasibilityproblems-2024\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-qin-wang-alternatedinertialalgorithmsforsplitfeasibilityproblems-2024')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TQW_NUMA24,\nauthor={Tan, Bing and Qin, Xiaolong and Wang, Xianfu},\ntitle={Alternated inertial algorithms for split feasibility problems},\njournal={Numerical Algorithms},\nyear={2024},\nvolume={95},\nnumber={2},\npages={773--812},\ndoi={10.1007/s11075-023-01589-8},\nurl={https://bingtan.me/files/paper/TQW-NUMA2024.pdf},\nabstract={We introduce four novel relaxed CQ algorithms with alternating inertial for solving split feasibility problems in real Hilbert spaces. The proposed algorithms employ a new non-monotonic adaptive step size criterion and utilize two different step sizes in each iteration. The weak convergence of the iterative sequences generated by the proposed algorithms is established under some weak conditions. Moreover, the Fejér monotonicity of the even subsequence with respect to the solution set is recovered. Two applications in signal denoising and image deblurring are given to illustrate the computational efficiency of our algorithms.},\nkeywords={Split feasibility problem,  CQ method,  Projection and contraction method,  Alternated inertial method,  Signal processing,  Image restoration},\nabbrev_source_title={Numer. Algorithms},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We introduce four novel relaxed CQ algorithms with alternating inertial for solving split feasibility problems in real Hilbert spaces. The proposed algorithms employ a new non-monotonic adaptive step size criterion and utilize two different step sizes in each iteration. The weak convergence of the iterative sequences generated by the proposed algorithms is established under some weak conditions. Moreover, the Fejér monotonicity of the even subsequence with respect to the solution set is recovered. Two applications in signal denoising and image deblurring are given to illustrate the computational efficiency of our algorithms.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"xie-cai-tan-inertialsubgradientextragradientmethodforsolvingpseudomonotoneequilibriumprobelmsandfixedpointproblemsinhilbertspaces-2024\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Xie, Z.; Cai, G.;  and <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Inertial subgradient extragradient method for solving pseudomonotone equilibrium probelms and fixed point problems in Hilbert spaces.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Optimization</i>, 73(5): 1329-1354.  2024.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/XCT-OPT2024.pdf\"\n     onclick=\"log_download('xie-cai-tan-inertialsubgradientextragradientmethodforsolvingpseudomonotoneequilibriumprobelmsandfixedpointproblemsinhilbertspaces-2024', 'https://bingtan.me/files/paper/XCT-OPT2024.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Inertial subgradient extragradient method for solving pseudomonotone equilibrium probelms and fixed point problems in Hilbert spaces [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1080/02331934.2022.2157677\"\n     onclick=\"log_download('xie-cai-tan-inertialsubgradientextragradientmethodforsolvingpseudomonotoneequilibriumprobelmsandfixedpointproblemsinhilbertspaces-2024', 'http://doi.org/10.1080/02331934.2022.2157677', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/xie-cai-tan-inertialsubgradientextragradientmethodforsolvingpseudomonotoneequilibriumprobelmsandfixedpointproblemsinhilbertspaces-2024\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('xie-cai-tan-inertialsubgradientextragradientmethodforsolvingpseudomonotoneequilibriumprobelmsandfixedpointproblemsinhilbertspaces-2024')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{XCT_OPT24,\nauthor={Xie, Zhongbing and Cai, Gang and Tan, Bing},\ntitle={Inertial subgradient extragradient method for solving pseudomonotone equilibrium probelms and fixed point problems in Hilbert spaces},\njournal={Optimization},\nyear={2024},\nvolume={73},\nnumber={5},\npages={1329-1354},\ndoi={10.1080/02331934.2022.2157677},\nurl={https://bingtan.me/files/paper/XCT-OPT2024.pdf},\nabstract={This paper proposes a new inertial subgradient extragradient method for solving equilibrium problems with pseudomonotone and Lipschitz-type bifunctions and fixed point problems for nonexpansive mappings in real Hilbert spaces. Precisely, we prove that the sequence generated by proposed algorithm converges strongly to a common solution of equilibrium problems and fixed point problems. We use an effective self-adaptive step size rule to accelerate the convergence process of our proposed iterative algorithm. Moreover, some numerical results are given to show the effectiveness of the proposed algorithm. The results obtained in this paper extend and improve many recent ones in the literature.},\nkeywords={Inertial method,  Subgradient extragradient method, Equilibrium probelm, Fixed point problem, Strong convergence},\nabbrev_source_title={Optimization},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This paper proposes a new inertial subgradient extragradient method for solving equilibrium problems with pseudomonotone and Lipschitz-type bifunctions and fixed point problems for nonexpansive mappings in real Hilbert spaces. Precisely, we prove that the sequence generated by proposed algorithm converges strongly to a common solution of equilibrium problems and fixed point problems. We use an effective self-adaptive step size rule to accelerate the convergence process of our proposed iterative algorithm. Moreover, some numerical results are given to show the effectiveness of the proposed algorithm. The results obtained in this paper extend and improve many recent ones in the literature.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-qin-analternatedinertialalgorithmwithweakandlinearconvergenceforsolvingmonotoneinclusions-2023\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Qin, X.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  An alternated inertial algorithm with weak and linear convergence for solving monotone inclusions.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Annals of Mathematical Sciences and Applications</i>, 8(2): 321–345.  2023.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TQ-AMSA2023.pdf\"\n     onclick=\"log_download('tan-qin-analternatedinertialalgorithmwithweakandlinearconvergenceforsolvingmonotoneinclusions-2023', 'https://bingtan.me/files/paper/TQ-AMSA2023.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"An alternated inertial algorithm with weak and linear convergence for solving monotone inclusions [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.4310/AMSA.2023.v8.n2.a7\"\n     onclick=\"log_download('tan-qin-analternatedinertialalgorithmwithweakandlinearconvergenceforsolvingmonotoneinclusions-2023', 'http://doi.org/10.4310/AMSA.2023.v8.n2.a7', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-qin-analternatedinertialalgorithmwithweakandlinearconvergenceforsolvingmonotoneinclusions-2023\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-qin-analternatedinertialalgorithmwithweakandlinearconvergenceforsolvingmonotoneinclusions-2023')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TQ_AMSA23,\nauthor={Tan, Bing and Qin, Xiaolong},\ntitle={An alternated inertial algorithm with weak and linear convergence for solving monotone inclusions},\njournal={Annals of Mathematical Sciences and Applications},\nyear={2023},\nvolume={8},\nnumber={2},\npages={321--345},\ndoi={10.4310/AMSA.2023.v8.n2.a7},\nurl={https://bingtan.me/files/paper/TQ-AMSA2023.pdf},\nabstract={Inertial-based methods have the drawback of not preserving the Fejér monotonicity of iterative sequences, which may result in slower convergence compared to their corresponding non-inertial versions. To overcome this issue, Mu and Peng [Stat. Optim. Inf. Comput. 3 (2015), 241–248; MR3393305] suggested an alternating inertial method that can recover the Fejér monotonicity of even subsequences. In this paper, we propose a modified version of the forward-backward algorithm with alternating inertial and relaxation effects to solve an inclusion problem in real Hilbert spaces. The weak and linear convergence of the presented algorithm is established under suitable and mild conditions on the involved operators and parameters. Furthermore, the Fejér monotonicity of even subsequences generated by the proposed algorithm with respect to the solution set is recovered. Finally, our tests on image restoration problems demonstrate the superiority of the proposed algorithm over some related results.},\nkeywords={Inclusion problems, Alternated inertial, Forward-backward method, Tseng&#x27;s method, Projection and contraction method, Linear convergence},\nabbrev_source_title={Ann. Math. Sci. Appl.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  Inertial-based methods have the drawback of not preserving the Fejér monotonicity of iterative sequences, which may result in slower convergence compared to their corresponding non-inertial versions. To overcome this issue, Mu and Peng [Stat. Optim. Inf. Comput. 3 (2015), 241–248; MR3393305] suggested an alternating inertial method that can recover the Fejér monotonicity of even subsequences. In this paper, we propose a modified version of the forward-backward algorithm with alternating inertial and relaxation effects to solve an inclusion problem in real Hilbert spaces. The weak and linear convergence of the presented algorithm is established under suitable and mild conditions on the involved operators and parameters. Furthermore, the Fejér monotonicity of even subsequences generated by the proposed algorithm with respect to the solution set is recovered. Finally, our tests on image restoration problems demonstrate the superiority of the proposed algorithm over some related results.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-qin-gibali-threeapproximationmethodsforsolvingconstraintvariationalinequalitiesandrelatedproblems-2023\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Qin, X.;  and Gibali, A.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Three approximation methods for solving constraint variational inequalities and related problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Pure and Applied Functional Analysis</i>, 8(3): 965–986.  2023.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TGQ_PAFA2023.pdf\"\n     onclick=\"log_download('tan-qin-gibali-threeapproximationmethodsforsolvingconstraintvariationalinequalitiesandrelatedproblems-2023', 'https://bingtan.me/files/paper/TGQ_PAFA2023.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Three approximation methods for solving constraint variational inequalities and related problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-qin-gibali-threeapproximationmethodsforsolvingconstraintvariationalinequalitiesandrelatedproblems-2023\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-qin-gibali-threeapproximationmethodsforsolvingconstraintvariationalinequalitiesandrelatedproblems-2023')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TGQ_PAFA23,\nauthor={Tan, Bing and Qin, Xiaolong and Gibali, Aviv},\ntitle={Three approximation methods for solving constraint variational inequalities and related problems},\njournal={Pure and Applied Functional Analysis},\nyear={2023},\nvolume={8},\nnumber={3},\npages={965--986},\nurl={https://bingtan.me/files/paper/TGQ_PAFA2023.pdf},\nabstract={In this paper, we present three new self-adaptive one-projection algorithms to find common solutions for the pseudo-monotone variational inequality problem and the fixed point problem of a demi-contractive mapping. Note that the suggested approaches use a non-monotonic self-adaptive step size so that they can work well without knowing the prior knowledge of the Lipschitz constant of the mapping. Strong convergence theorems of the proposed iterative schemes are established in real Hilbert spaces. Several mathematical experiments are reported to demonstrate the numerical behavior of the suggested algorithms and compare them with the existing ones. Finally, the suggested methods are used to solve optimal control problems.},\nkeywords={Variational inequality, Fixed point, Extragradient method, Hybrid steepest descent method, Pseudomonotone mapping},\nabbrev_source_title={Pure Appl. Funct. Anal.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we present three new self-adaptive one-projection algorithms to find common solutions for the pseudo-monotone variational inequality problem and the fixed point problem of a demi-contractive mapping. Note that the suggested approaches use a non-monotonic self-adaptive step size so that they can work well without knowing the prior knowledge of the Lipschitz constant of the mapping. Strong convergence theorems of the proposed iterative schemes are established in real Hilbert spaces. Several mathematical experiments are reported to demonstrate the numerical behavior of the suggested algorithms and compare them with the existing ones. Finally, the suggested methods are used to solve optimal control problems.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-li-cho-inertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalitieswithnonlipschitzoperatorsandapplications-2023\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Li, S.;  and Cho, S. Y.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Inertial projection and contraction methods for pseudomonotone variational inequalities with non-Lipschitz operators and applications.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Applicable Analysis</i>, 102(4): 1199–1221.  2023.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TLC-AA2023.pdf\"\n     onclick=\"log_download('tan-li-cho-inertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalitieswithnonlipschitzoperatorsandapplications-2023', 'https://bingtan.me/files/paper/TLC-AA2023.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Inertial projection and contraction methods for pseudomonotone variational inequalities with non-Lipschitz operators and applications [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1080/00036811.2021.1979219\"\n     onclick=\"log_download('tan-li-cho-inertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalitieswithnonlipschitzoperatorsandapplications-2023', 'http://doi.org/10.1080/00036811.2021.1979219', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-li-cho-inertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalitieswithnonlipschitzoperatorsandapplications-2023\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-li-cho-inertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalitieswithnonlipschitzoperatorsandapplications-2023')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TLC_AA23,\nauthor={Tan, Bing and Li, Songxiao and Cho, Sun Y.},\ntitle={Inertial projection and contraction methods for pseudomonotone variational inequalities with non-Lipschitz operators and applications},\njournal={Applicable Analysis},\nyear={2023},\nvolume={102},\nnumber={4},\ndoi={10.1080/00036811.2021.1979219},\npages={1199--1221},\nurl={https://bingtan.me/files/paper/TLC-AA2023.pdf},\nabstract={In this paper, some new accelerated iterative schemes are proposed to solve the variational inequality problem with a pseudomonotone and uniformly continuous operator in real Hilbert spaces. Strong convergence theorems of the suggested algorithms are obtained without the prior knowledge of the Lipschitz constant of the operator. Some numerical experiments and applications are performed to illustrate the advantages of the proposed methods with respect to several related ones.},\nkeywords={Inertial extragradient method,  Projection and contraction method,  Pseudomonotone operator,  Non-Lipschitz operator,  Variational inequality problem},\nabbrev_source_title={Appl. Anal.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, some new accelerated iterative schemes are proposed to solve the variational inequality problem with a pseudomonotone and uniformly continuous operator in real Hilbert spaces. Strong convergence theorems of the suggested algorithms are obtained without the prior knowledge of the Lipschitz constant of the operator. Some numerical experiments and applications are performed to illustrate the advantages of the proposed methods with respect to several related ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-sunthrayuth-cholamjiak-cho-modifiedinertialextragradientmethodsforfindingminimumnormsolutionofthevariationalinequalityproblemwithapplicationstooptimalcontrolproblem-2023\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Sunthrayuth, P.; Cholamjiak, P.;  and Cho, Y. J.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Modified inertial extragradient methods for finding minimum-norm solution of the variational inequality problem with applications to optimal control problem.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>International Journal of Computer Mathematics</i>, 100(3): 525–545.  2023.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TSCC-IJCM23.pdf\"\n     onclick=\"log_download('tan-sunthrayuth-cholamjiak-cho-modifiedinertialextragradientmethodsforfindingminimumnormsolutionofthevariationalinequalityproblemwithapplicationstooptimalcontrolproblem-2023', 'https://bingtan.me/files/paper/TSCC-IJCM23.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Modified inertial extragradient methods for finding minimum-norm solution of the variational inequality problem with applications to optimal control problem [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1080/00207160.2022.2137672\"\n     onclick=\"log_download('tan-sunthrayuth-cholamjiak-cho-modifiedinertialextragradientmethodsforfindingminimumnormsolutionofthevariationalinequalityproblemwithapplicationstooptimalcontrolproblem-2023', 'http://doi.org/10.1080/00207160.2022.2137672', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-sunthrayuth-cholamjiak-cho-modifiedinertialextragradientmethodsforfindingminimumnormsolutionofthevariationalinequalityproblemwithapplicationstooptimalcontrolproblem-2023\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-sunthrayuth-cholamjiak-cho-modifiedinertialextragradientmethodsforfindingminimumnormsolutionofthevariationalinequalityproblemwithapplicationstooptimalcontrolproblem-2023')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TSCC_IJCM23,\nauthor={Tan, Bing and Sunthrayuth, Pongsakorn and Cholamjiak, Prasit and  Cho, Yeol J.},\ntitle={Modified inertial extragradient methods for finding minimum-norm solution of the variational inequality problem with applications to optimal control problem},\njournal={International Journal of Computer Mathematics},\nyear={2023},\nvolume={100},\nnumber={3},\npages={525--545},\ndoi={10.1080/00207160.2022.2137672},\nurl={https://bingtan.me/files/paper/TSCC-IJCM23.pdf},\nabstract={In order to discover the minimum-norm solution of the pseudomonotone variational inequality problem in a real Hilbert space, we provide two variants of the inertial extragradient approach with a novel generalized adaptive step size. Two of the suggested algorithms make use of the projection and contraction methods. We demonstrate several strong convergence findings without requiring the prior knowledge of the Lipschitz constant of the mapping. Finally, we give a number of numerical examples that highlight the benefits and effectiveness of the suggested algorithms and how they may be used to solve the optimal control problem.},\nkeywords={Variational inequality problem, Optimal control problem, Inertial method, Projection and contraction method},\nabbrev_source_title={Int. J. Comput. Math.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In order to discover the minimum-norm solution of the pseudomonotone variational inequality problem in a real Hilbert space, we provide two variants of the inertial extragradient approach with a novel generalized adaptive step size. Two of the suggested algorithms make use of the projection and contraction methods. We demonstrate several strong convergence findings without requiring the prior knowledge of the Lipschitz constant of the mapping. Finally, we give a number of numerical examples that highlight the benefits and effectiveness of the suggested algorithms and how they may be used to solve the optimal control problem.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-li-adaptiveinertialsubgradientextragradientmethodsforfindingminimumnormsolutionsofpseudomonotonevariationalinequalities-2023\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Adaptive inertial subgradient extragradient methods for finding minimum-norm solutions of pseudomonotone variational inequalities.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Industrial and Management Optimization</i>, 19(10): 7640–7659.  2023.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TL-JIMO2023.pdf\"\n     onclick=\"log_download('tan-li-adaptiveinertialsubgradientextragradientmethodsforfindingminimumnormsolutionsofpseudomonotonevariationalinequalities-2023', 'https://bingtan.me/files/paper/TL-JIMO2023.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Adaptive inertial subgradient extragradient methods for finding minimum-norm solutions of pseudomonotone variational inequalities [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.3934/jimo.2022060\"\n     onclick=\"log_download('tan-li-adaptiveinertialsubgradientextragradientmethodsforfindingminimumnormsolutionsofpseudomonotonevariationalinequalities-2023', 'http://doi.org/10.3934/jimo.2022060', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-li-adaptiveinertialsubgradientextragradientmethodsforfindingminimumnormsolutionsofpseudomonotonevariationalinequalities-2023\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-li-adaptiveinertialsubgradientextragradientmethodsforfindingminimumnormsolutionsofpseudomonotonevariationalinequalities-2023')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TL_JIMO23,\nauthor={Tan, Bing and Li, Songxiao},\ntitle={Adaptive inertial subgradient extragradient methods for finding minimum-norm solutions of pseudomonotone variational inequalities},\njournal={Journal of Industrial and Management Optimization},\nyear={2023},\nvolume={19},\nnumber={10},\npages={7640--7659},\ndoi={10.3934/jimo.2022060},\nurl={https://bingtan.me/files/paper/TL-JIMO2023.pdf},\nabstract={In this paper, four modified inertial subgradient extragradient methods with a new non-monotonic step size criterion are investigated for pseudomonotone variational inequality problems in real Hilbert spaces. Our algorithms employ two different step sizes in each iteration to update the values of iterative sequences, and they work well without the prior information about the Lipschitz constant of the operator. Strong convergence theorems of the proposed iterative schemes are established under some suitable and mild conditions. Some numerical examples are provided to demonstrate the computational efficiency and advantages of the proposed methods over other known ones.},\nkeywords={Variational inequality problem, Inertial method, Extragradient method, Pseudomonotone operator, Non-Lipschitz operator},\nabbrev_source_title={J. Ind. Manag. Optim.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, four modified inertial subgradient extragradient methods with a new non-monotonic step size criterion are investigated for pseudomonotone variational inequality problems in real Hilbert spaces. Our algorithms employ two different step sizes in each iteration to update the values of iterative sequences, and they work well without the prior information about the Lipschitz constant of the operator. Strong convergence theorems of the proposed iterative schemes are established under some suitable and mild conditions. Some numerical examples are provided to demonstrate the computational efficiency and advantages of the proposed methods over other known ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"zhou-tan-li-inertialalgorithmswithadaptivestepsizesforsplitvariationalinclusionproblemsandtheirapplicationstosignalrecoveryproblem-2023\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Zhou, Z.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Inertial algorithms with adaptive stepsizes for split variational inclusion problems and their applications to signal recovery problem.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Mathematical Methods in the Applied Sciences</i>, doi:10.1002/mma.9436.  2023.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/ZTL-MMAS2023.pdf\"\n     onclick=\"log_download('zhou-tan-li-inertialalgorithmswithadaptivestepsizesforsplitvariationalinclusionproblemsandtheirapplicationstosignalrecoveryproblem-2023', 'https://bingtan.me/files/paper/ZTL-MMAS2023.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Inertial algorithms with adaptive stepsizes for split variational inclusion problems and their applications to signal recovery problem [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1002/mma.9436\"\n     onclick=\"log_download('zhou-tan-li-inertialalgorithmswithadaptivestepsizesforsplitvariationalinclusionproblemsandtheirapplicationstosignalrecoveryproblem-2023', 'http://doi.org/10.1002/mma.9436', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/zhou-tan-li-inertialalgorithmswithadaptivestepsizesforsplitvariationalinclusionproblemsandtheirapplicationstosignalrecoveryproblem-2023\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('zhou-tan-li-inertialalgorithmswithadaptivestepsizesforsplitvariationalinclusionproblemsandtheirapplicationstosignalrecoveryproblem-2023')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{ZTL_MMAS23,\nauthor={Zhou, Zheng and Tan, Bing and Li, Songxiao},\ntitle={Inertial algorithms with adaptive stepsizes for split variational inclusion problems and their applications to signal recovery problem},\njournal={Mathematical Methods in the Applied Sciences},\nyear={2023},\nvolume={doi:10.1002/mma.9436},\ndoi={10.1002/mma.9436},\nurl={https://bingtan.me/files/paper/ZTL-MMAS2023.pdf},\nabstract={With the help of the Meir-Keeler contraction method and the Mann-type method, two adaptive inertial iterative schemes are introduced for finding solutions of the split variational inclusion problem in Hilbert spaces. The strong convergence of the suggested algorithms is guaranteed by a new stepsize criterion that does not require calculation of the bounded linear operator norm. Some numerical experiments and applications in signal recovery problems are given to demonstrate the efficiency of the proposed algorithms.},\nkeywords={Adaptive stepsize, Inertial method, Mann method, Meir-Keeler contraction, Signal recovery, Split variational inclusion problem},\nabbrev_source_title={Math. Methods Appl. Sci.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  With the help of the Meir-Keeler contraction method and the Mann-type method, two adaptive inertial iterative schemes are introduced for finding solutions of the split variational inclusion problem in Hilbert spaces. The strong convergence of the suggested algorithms is guaranteed by a new stepsize criterion that does not require calculation of the bounded linear operator norm. Some numerical experiments and applications in signal recovery problems are given to demonstrate the efficiency of the proposed algorithms.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"luo-tan-li-inertialsplittingalgorithmsfornonlinearoperatorsofpseudocontractiveandaccretivetypes-2023\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Luo, Y.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Inertial splitting algorithms for nonlinear operators of pseudocontractive and accretive types.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Optimization</i>, 72(3): 647–675.  2023.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/LTL-OPT2023.pdf\"\n     onclick=\"log_download('luo-tan-li-inertialsplittingalgorithmsfornonlinearoperatorsofpseudocontractiveandaccretivetypes-2023', 'https://bingtan.me/files/paper/LTL-OPT2023.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Inertial splitting algorithms for nonlinear operators of pseudocontractive and accretive types [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1080/02331934.2021.1981896\"\n     onclick=\"log_download('luo-tan-li-inertialsplittingalgorithmsfornonlinearoperatorsofpseudocontractiveandaccretivetypes-2023', 'http://doi.org/10.1080/02331934.2021.1981896', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/luo-tan-li-inertialsplittingalgorithmsfornonlinearoperatorsofpseudocontractiveandaccretivetypes-2023\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('luo-tan-li-inertialsplittingalgorithmsfornonlinearoperatorsofpseudocontractiveandaccretivetypes-2023')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{LTL_OPT23,\nauthor={Luo, Yinglin and Tan, Bing and Li, Songxiao},\ntitle={Inertial splitting algorithms for nonlinear operators of pseudocontractive and accretive types},\njournal={Optimization},\nyear={2023},\nvolume={72},\nnumber={3},\npages={647--675},\ndoi={10.1080/02331934.2021.1981896},\nurl={https://bingtan.me/files/paper/LTL-OPT2023.pdf},\nabstract={In this paper, inertial splitting algorithms for nonlinear operators of pseudocontractive and accretive types are proposed. Weak and strong convergence theorems are established in uniformly convex and $q$-uniformly smooth Banach spaces. Numerical examples are given to illustrate the effectiveness of our proposed algorithms.},\nkeywords={Accretive operator,  Banach space,  Inertial method,  Strict pseudo-contraction,  Strong convergence},\nabbrev_source_title={Optimization},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, inertial splitting algorithms for nonlinear operators of pseudocontractive and accretive types are proposed. Weak and strong convergence theorems are established in uniformly convex and $q$-uniformly smooth Banach spaces. Numerical examples are given to illustrate the effectiveness of our proposed algorithms.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"zhou-cai-tan-dong-amodifiedgeneralizedversionofprojectedreflectedgradientmethodinhilbertspaces-2023\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Zhou, X.; Cai, G.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Dong, Q. L.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  A modified generalized version of projected reflected gradient method in Hilbert spaces.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Numerical Algorithms</i>, doi:10.1007/s11075-023-01566-1.  2023.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/ZCTD-NUMA2023.pdf\"\n     onclick=\"log_download('zhou-cai-tan-dong-amodifiedgeneralizedversionofprojectedreflectedgradientmethodinhilbertspaces-2023', 'https://bingtan.me/files/paper/ZCTD-NUMA2023.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"A modified generalized version of projected reflected gradient method in Hilbert spaces [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s11075-023-01566-1\"\n     onclick=\"log_download('zhou-cai-tan-dong-amodifiedgeneralizedversionofprojectedreflectedgradientmethodinhilbertspaces-2023', 'http://doi.org/10.1007/s11075-023-01566-1', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/zhou-cai-tan-dong-amodifiedgeneralizedversionofprojectedreflectedgradientmethodinhilbertspaces-2023\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('zhou-cai-tan-dong-amodifiedgeneralizedversionofprojectedreflectedgradientmethodinhilbertspaces-2023')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{ZCTD_NUMA23,\nauthor={Zhou, Xiaolin and Cai, Gang and Tan, Bing and Dong, Qiao L.},\ntitle={A modified generalized version of projected reflected gradient method in Hilbert spaces},\njournal={Numerical Algorithms},\nyear={2023},\nvolume={doi:10.1007/s11075-023-01566-1},\ndoi={10.1007/s11075-023-01566-1},\nurl={https://bingtan.me/files/paper/ZCTD-NUMA2023.pdf},\nabstract={This article is concerned with a universal version of projected reflected gradient method with new step size for solving variational inequality problem in Hilbert spaces. Under appropriate assumptions controlled by the operators and parameters, we acquire the weak convergence of the proposed algorithm. We establish an R-linear convergence rate of our method on the condition that the relevant mapping is strongly monotone. We rework our first algorithm so that it can be simplified to several generalized methods in the literature. The efficacy and availability of our proposed iterative scheme are demonstrated in numerical experiments.},\nkeywords={Projected reflected gradient method, Variational inequality, Weak and linear convergence, Hilbert spaces},\nabbrev_source_title={Numer. Algorithms},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This article is concerned with a universal version of projected reflected gradient method with new step size for solving variational inequality problem in Hilbert spaces. Under appropriate assumptions controlled by the operators and parameters, we acquire the weak convergence of the proposed algorithm. We establish an R-linear convergence rate of our method on the condition that the relevant mapping is strongly monotone. We rework our first algorithm so that it can be simplified to several generalized methods in the literature. The efficacy and availability of our proposed iterative scheme are demonstrated in numerical experiments.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"hu-wang-tan-wang-inertialiterativemethodforsolvingvariationalinequalityproblemsofpseudomonotoneoperatorsandfixedpointproblemsofnonexpansivemappingsinhilbertspaces-2023\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Hu, S.; Wang, Y.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Wang, F.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Inertial iterative method for solving variational inequality problems of pseudo-monotone operators and fixed point problems of nonexpansive mappings in Hilbert spaces.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Industrial and Management Optimization</i>, 19(4): 2655–2675.  2023.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/HWTW-JIMO2023.pdf\"\n     onclick=\"log_download('hu-wang-tan-wang-inertialiterativemethodforsolvingvariationalinequalityproblemsofpseudomonotoneoperatorsandfixedpointproblemsofnonexpansivemappingsinhilbertspaces-2023', 'https://bingtan.me/files/paper/HWTW-JIMO2023.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Inertial iterative method for solving variational inequality problems of pseudo-monotone operators and fixed point problems of nonexpansive mappings in Hilbert spaces [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.3934/jimo.2022060\"\n     onclick=\"log_download('hu-wang-tan-wang-inertialiterativemethodforsolvingvariationalinequalityproblemsofpseudomonotoneoperatorsandfixedpointproblemsofnonexpansivemappingsinhilbertspaces-2023', 'http://doi.org/10.3934/jimo.2022060', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/hu-wang-tan-wang-inertialiterativemethodforsolvingvariationalinequalityproblemsofpseudomonotoneoperatorsandfixedpointproblemsofnonexpansivemappingsinhilbertspaces-2023\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('hu-wang-tan-wang-inertialiterativemethodforsolvingvariationalinequalityproblemsofpseudomonotoneoperatorsandfixedpointproblemsofnonexpansivemappingsinhilbertspaces-2023')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{HWTW_JIMO23,\nauthor={Hu, Shaotao and Wang, Yuanheng and Tan, Bing and Wang, Fenghui},\ntitle={Inertial iterative method for solving variational inequality problems of pseudo-monotone operators and fixed point problems of nonexpansive mappings in {H}ilbert spaces},\njournal={Journal of Industrial and Management Optimization},\nyear={2023},\nvolume={19},\nnumber={4},\npages={2655--2675},\ndoi={10.3934/jimo.2022060},\nurl={https://bingtan.me/files/paper/HWTW-JIMO2023.pdf},\nabstract={In this paper, we propose a new inertial viscosity iterative algorithm for solving the variational inequality problem with a pseudo-monotone operator and the fixed point problem involving a nonexpansive mapping in real Hilbert spaces. The advantage of the proposed algorithm is that it can work without the prior knowledge of the Lipschitz constant of the mapping. The strong convergence of the sequence generated by the proposed algorithm is proved under some suitable assumptions imposed on the parameters. Some numerical experiments are given to support our main results.},\nkeywords={Inertial method,  Viscosity method,  Strong convergence, Variational inequality problem, Fixed point problem, Nonexpansive mapping, Pseudomonotone operator},\nabbrev_source_title={J. Ind. Manag. Optim.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we propose a new inertial viscosity iterative algorithm for solving the variational inequality problem with a pseudo-monotone operator and the fixed point problem involving a nonexpansive mapping in real Hilbert spaces. The advantage of the proposed algorithm is that it can work without the prior knowledge of the Lipschitz constant of the mapping. The strong convergence of the sequence generated by the proposed algorithm is proved under some suitable assumptions imposed on the parameters. Some numerical experiments are given to support our main results.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-qin-cho-revisitingsubgradientextragradientmethodsforsolvingvariationalinequalities-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Qin, X.;  and Cho, S. Y.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Revisiting subgradient extragradient methods for solving variational inequalities.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Numerical Algorithms</i>, 90(4): 1593–1615.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TQC-NUMA2022.pdf\"\n     onclick=\"log_download('tan-qin-cho-revisitingsubgradientextragradientmethodsforsolvingvariationalinequalities-2022', 'https://bingtan.me/files/paper/TQC-NUMA2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Revisiting subgradient extragradient methods for solving variational inequalities [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s11075-021-01243-1\"\n     onclick=\"log_download('tan-qin-cho-revisitingsubgradientextragradientmethodsforsolvingvariationalinequalities-2022', 'http://doi.org/10.1007/s11075-021-01243-1', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-qin-cho-revisitingsubgradientextragradientmethodsforsolvingvariationalinequalities-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>2 downloads</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-qin-cho-revisitingsubgradientextragradientmethodsforsolvingvariationalinequalities-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TQC_NUMA22,\nauthor={Tan, Bing and Qin, Xiaolong and Cho, Sun Y.},\ntitle={Revisiting subgradient extragradient methods for solving variational inequalities},\njournal={Numerical Algorithms},\nyear={2022},\nvolume={90},\nnumber={4},\npages={1593--1615},\ndoi={10.1007/s11075-021-01243-1},\nurl={https://bingtan.me/files/paper/TQC-NUMA2022.pdf},\nabstract={In this paper, several extragradient algorithms with inertial effects and adaptive non-monotonic step sizes are proposed to solve pseudomonotone variational inequalities in real Hilbert spaces. The strong convergence of the proposed methods is established without the prior knowledge of the Lipschitz constant of the mapping. Some numerical experiments are given to illustrate the advantages and efficiency of the proposed schemes over previously known ones.},\nkeywords={Armijo stepsize,  Inertial extragradient method,  Non-Lipschitz operator,  Pseudomonotone operator,  Variational inequality problem},\nabbrev_source_title={Numer. Algorithms},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, several extragradient algorithms with inertial effects and adaptive non-monotonic step sizes are proposed to solve pseudomonotone variational inequalities in real Hilbert spaces. The strong convergence of the proposed methods is established without the prior knowledge of the Lipschitz constant of the mapping. Some numerical experiments are given to illustrate the advantages and efficiency of the proposed schemes over previously known ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-qin-yao-strongconvergenceofinertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalitieswithapplicationstooptimalcontrolproblems-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Qin, X.;  and Yao, J. C.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Strong convergence of inertial projection and contraction methods for pseudomonotone variational inequalities with applications to optimal control problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Global Optimization</i>, 82(3): 523–557.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TQY-JOGO2022.pdf\"\n     onclick=\"log_download('tan-qin-yao-strongconvergenceofinertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalitieswithapplicationstooptimalcontrolproblems-2022', 'https://bingtan.me/files/paper/TQY-JOGO2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Strong convergence of inertial projection and contraction methods for pseudomonotone variational inequalities with applications to optimal control problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s10898-021-01095-y\"\n     onclick=\"log_download('tan-qin-yao-strongconvergenceofinertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalitieswithapplicationstooptimalcontrolproblems-2022', 'http://doi.org/10.1007/s10898-021-01095-y', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-qin-yao-strongconvergenceofinertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalitieswithapplicationstooptimalcontrolproblems-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-qin-yao-strongconvergenceofinertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalitieswithapplicationstooptimalcontrolproblems-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TQY_JOGO22,\nauthor={Tan, Bing and Qin, Xiaolong and Yao, Jen C.},\ntitle={Strong convergence of inertial projection and contraction methods for pseudomonotone variational inequalities with applications to optimal control problems},\njournal={Journal of Global Optimization},\nyear={2022},\nvolume={82},\nnumber={3},\npages={523--557},\ndoi={10.1007/s10898-021-01095-y},\nurl={https://bingtan.me/files/paper/TQY-JOGO2022.pdf},\nabstract={This paper investigates some inertial projection and contraction methods for solving pseudomonotone variational inequality problems in real Hilbert spaces. The algorithms use a new non-monotonic step size so that they can work without the prior knowledge of the Lipschitz constant of the operator. Strong convergence theorems of the suggested algorithms are obtained under some suitable conditions. Some numerical experiments in finite- and infinite-dimensional spaces and applications in optimal control problems are implemented to demonstrate the performance of the suggested schemes and we also compare them with several related results.},\nkeywords={Inertial method,  Optimal control problem,  Projection and contraction method,  Pseudomonotone operator,  Subgradient extragradient method,  Variational inequality problem},\nabbrev_source_title={J. Global Optim.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This paper investigates some inertial projection and contraction methods for solving pseudomonotone variational inequality problems in real Hilbert spaces. The algorithms use a new non-monotonic step size so that they can work without the prior knowledge of the Lipschitz constant of the operator. Strong convergence theorems of the suggested algorithms are obtained under some suitable conditions. Some numerical experiments in finite- and infinite-dimensional spaces and applications in optimal control problems are implemented to demonstrate the performance of the suggested schemes and we also compare them with several related results.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-qin-modifiedinertialprojectionandcontractionalgorithmsforsolvingvariationalinequalityproblemswithnonlipschitzcontinuousoperators-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Qin, X.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Modified inertial projection and contraction algorithms for solving variational inequality problems with non-Lipschitz continuous operators.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Analysis and Mathematical Physics</i>, 12(1): 26.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TQ-AMP2022.pdf\"\n     onclick=\"log_download('tan-qin-modifiedinertialprojectionandcontractionalgorithmsforsolvingvariationalinequalityproblemswithnonlipschitzcontinuousoperators-2022', 'https://bingtan.me/files/paper/TQ-AMP2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Modified inertial projection and contraction algorithms for solving variational inequality problems with non-Lipschitz continuous operators [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s13324-021-00638-6\"\n     onclick=\"log_download('tan-qin-modifiedinertialprojectionandcontractionalgorithmsforsolvingvariationalinequalityproblemswithnonlipschitzcontinuousoperators-2022', 'http://doi.org/10.1007/s13324-021-00638-6', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-qin-modifiedinertialprojectionandcontractionalgorithmsforsolvingvariationalinequalityproblemswithnonlipschitzcontinuousoperators-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-qin-modifiedinertialprojectionandcontractionalgorithmsforsolvingvariationalinequalityproblemswithnonlipschitzcontinuousoperators-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TQ_AMP22,\nauthor={Tan, Bing and Qin, Xiaolong},\ntitle={Modified inertial projection and contraction algorithms for solving variational inequality problems with non-Lipschitz continuous operators},\njournal={Analysis and Mathematical Physics},\nyear={2022},\nvolume={12},\nnumber={1},\ndoi={10.1007/s13324-021-00638-6},\npages={26},\nurl={https://bingtan.me/files/paper/TQ-AMP2022.pdf},\nabstract={In this paper, we present four modified inertial projection and contraction methods to solve the variational inequality problem with a pseudo-monotone and non-Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems of the proposed algorithms are established without the prior knowledge of the Lipschitz constant of the operator. Several numerical experiments and the applications to optimal control problems are provided to verify the advantages and efficiency of the proposed algorithms.},\nkeywords={Inertial method,  Projection and contraction method,  Pseudomonotone operator,  Subgradient extragradient method,  Non-Lipschitz operator,  Variational inequality problem},\nabbrev_source_title={Anal. Math. Phys.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we present four modified inertial projection and contraction methods to solve the variational inequality problem with a pseudo-monotone and non-Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems of the proposed algorithms are established without the prior knowledge of the Lipschitz constant of the operator. Several numerical experiments and the applications to optimal control problems are provided to verify the advantages and efficiency of the proposed algorithms.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-petruel-qin-yao-globalandlinearconvergenceofalternatedinertialsingleprojectionalgorithmsforpseudomonotonevariationalinequalities-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Petruşel, A.; Qin, X.;  and Yao, J. C.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Global and linear convergence of alternated inertial single projection algorithms for pseudo-monotone variational inequalities.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Fixed Point Theory</i>, 23(1): 391–426.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TPQY-FPT2022.pdf\"\n     onclick=\"log_download('tan-petruel-qin-yao-globalandlinearconvergenceofalternatedinertialsingleprojectionalgorithmsforpseudomonotonevariationalinequalities-2022', 'https://bingtan.me/files/paper/TPQY-FPT2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Global and linear convergence of alternated inertial single projection algorithms for pseudo-monotone variational inequalities [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.24193/fpt-ro.2022.1.25\"\n     onclick=\"log_download('tan-petruel-qin-yao-globalandlinearconvergenceofalternatedinertialsingleprojectionalgorithmsforpseudomonotonevariationalinequalities-2022', 'http://doi.org/10.24193/fpt-ro.2022.1.25', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-petruel-qin-yao-globalandlinearconvergenceofalternatedinertialsingleprojectionalgorithmsforpseudomonotonevariationalinequalities-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>2 downloads</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-petruel-qin-yao-globalandlinearconvergenceofalternatedinertialsingleprojectionalgorithmsforpseudomonotonevariationalinequalities-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TPQY_FPT22,\nauthor={Tan, Bing and Petruşel, Adrian and Qin, Xiaolong and Yao, Jen C.},\ntitle={Global and linear convergence of alternated inertial single projection algorithms for pseudo-monotone variational inequalities},\njournal={Fixed Point Theory},\nyear={2022},\nvolume={23},\nnumber={1},\npages={391--426},\ndoi={10.24193/fpt-ro.2022.1.25},\nurl={https://bingtan.me/files/paper/TPQY-FPT2022.pdf},\nabstract={In this paper, we investigate three new relaxed single projection methods with alternating inertial extrapolation steps and adaptive non-monotonic step sizes for solving pseudo-monotone variational inequalities in real Hilbert spaces. The proposed algorithms need to compute the projection on the feasible set only once in each iteration and they can work adaptively without the prior information of the Lipschitz constant of the mapping. The weak convergence theorems of the proposed iterative schemes are established under some appropriate conditions imposed on the parameters. These methods recover the Fejér monotonicity of the even subsequence with respect to the solution and obtain linear convergence rates. Finally, some numerical experiments and applications to optimal control problems are provided to demonstrate the advantages and efficiency of the proposed methods compared to some recent related ones.},\nkeywords={Adaptive stepsize,  Alternated inertial method,  Projection and contraction method,  Pseudomonotone operator,  Subgradient extragradient method,  Variational inequality problem},\nabbrev_source_title={Fixed Point Theory},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we investigate three new relaxed single projection methods with alternating inertial extrapolation steps and adaptive non-monotonic step sizes for solving pseudo-monotone variational inequalities in real Hilbert spaces. The proposed algorithms need to compute the projection on the feasible set only once in each iteration and they can work adaptively without the prior information of the Lipschitz constant of the mapping. The weak convergence theorems of the proposed iterative schemes are established under some appropriate conditions imposed on the parameters. These methods recover the Fejér monotonicity of the even subsequence with respect to the solution and obtain linear convergence rates. Finally, some numerical experiments and applications to optimal control problems are provided to demonstrate the advantages and efficiency of the proposed methods compared to some recent related ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-qin-adaptivemodifiedinertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalities-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Qin, X.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Adaptive modified inertial projection and contraction methods for pseudomonotone variational inequalities.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Applied and Numerical Optimization</i>, 4(2): 221–243.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TQ-JANO2022.pdf\"\n     onclick=\"log_download('tan-qin-adaptivemodifiedinertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalities-2022', 'https://bingtan.me/files/paper/TQ-JANO2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Adaptive modified inertial projection and contraction methods for pseudomonotone variational inequalities [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.23952/jano.4.2022.2.08\"\n     onclick=\"log_download('tan-qin-adaptivemodifiedinertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalities-2022', 'http://doi.org/10.23952/jano.4.2022.2.08', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-qin-adaptivemodifiedinertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalities-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-qin-adaptivemodifiedinertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalities-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TQ_JANO22,\nauthor={Tan, Bing and Qin, Xiaolong},\ntitle={Adaptive modified inertial projection and contraction methods for pseudomonotone variational inequalities},\njournal={Journal of Applied and Numerical Optimization},\nyear={2022},\nvolume={4},\nnumber={2},\npages={221--243},\ndoi={10.23952/jano.4.2022.2.08},\nurl={https://bingtan.me/files/paper/TQ-JANO2022.pdf},\nabstract={To handle pseudomonotone variational inequality problems in real Hilbert spaces, four modified inertial projection and contraction algorithms with non-monotonic step sizes are suggested in this paper. The proposed algorithms take advantage of a novel non-monotonic step size criteria, allowing them to work without previous knowledge of the Lipschitz constant of the mapping involved. Under certain situations, the strong convergence of the iterative sequences generated by the suggested algorithms is established. Finally, several numerical experiments are offered to validate the theoretical conclusions.},\nkeywords={Inertial method, Pseudomonotone operator, Projection and contraction method, Subgradient extragradient method, Variational inequality problem},\nabbrev_source_title={J. Appl. Numer. Optim.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  To handle pseudomonotone variational inequality problems in real Hilbert spaces, four modified inertial projection and contraction algorithms with non-monotonic step sizes are suggested in this paper. The proposed algorithms take advantage of a novel non-monotonic step size criteria, allowing them to work without previous knowledge of the Lipschitz constant of the mapping involved. Under certain situations, the strong convergence of the iterative sequences generated by the suggested algorithms is established. Finally, several numerical experiments are offered to validate the theoretical conclusions.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-qin-selfadaptiveviscositytypeinertialextragradientalgorithmsforsolvingvariationalinequalitieswithapplications-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Qin, X.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Self adaptive viscosity-type inertial extragradient algorithms for solving variational inequalities with applications.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Mathematical Modelling and Analysis</i>, 27(1): 41–58.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><span style=\"color: red\">(<s>ESI Highly Cited Paper</s>)</span></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TQ-MMA2022.pdf\"\n     onclick=\"log_download('tan-qin-selfadaptiveviscositytypeinertialextragradientalgorithmsforsolvingvariationalinequalitieswithapplications-2022', 'https://bingtan.me/files/paper/TQ-MMA2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Self adaptive viscosity-type inertial extragradient algorithms for solving variational inequalities with applications [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.3846/mma.2022.13846\"\n     onclick=\"log_download('tan-qin-selfadaptiveviscositytypeinertialextragradientalgorithmsforsolvingvariationalinequalitieswithapplications-2022', 'http://doi.org/10.3846/mma.2022.13846', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-qin-selfadaptiveviscositytypeinertialextragradientalgorithmsforsolvingvariationalinequalitieswithapplications-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-qin-selfadaptiveviscositytypeinertialextragradientalgorithmsforsolvingvariationalinequalitieswithapplications-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TQ_MMA22,\nauthor={Tan, Bing and Qin, Xiaolong},\ntitle={Self adaptive viscosity-type inertial extragradient algorithms for solving variational inequalities with applications},\njournal={Mathematical Modelling and Analysis},\nyear={2022},\nvolume={27},\nnumber={1},\npages={41--58},\ndoi={10.3846/mma.2022.13846},\nurl={https://bingtan.me/files/paper/TQ-MMA2022.pdf},\nabstract={In this paper, we introduce two new inertial extragradient algorithms with non-monotonic stepsizes for solving monotone and Lipschitz continuous variational inequality problems in real Hilbert spaces. Strong convergence theorems of the suggested iterative schemes are established without the prior knowledge of the Lipschitz constant of the mapping. Finally, some numerical examples are provided to illustrate the efficiency and advantages of the proposed algorithms and compare them with some related ones.},\nkeywords={Inertial method, Subgradient extragradient method,  Tseng&#x27;s extragradient method,  Optimal control problem,  Variational inequality problem,  Viscosity method},\nabbrev_source_title={Math. Model. Anal.},\nbibbase_note={&lt;span style=&quot;color: red&quot;&gt;(&lt;s&gt;ESI Highly Cited Paper&lt;/s&gt;)&lt;/span&gt;},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we introduce two new inertial extragradient algorithms with non-monotonic stepsizes for solving monotone and Lipschitz continuous variational inequality problems in real Hilbert spaces. Strong convergence theorems of the suggested iterative schemes are established without the prior knowledge of the Lipschitz constant of the mapping. Finally, some numerical examples are provided to illustrate the efficiency and advantages of the proposed algorithms and compare them with some related ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-liu-qin-strongconvergenceofinertialextragradientalgorithmsforsolvingvariationalinequalitiesandfixedpointproblems-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Liu, L.;  and Qin, X.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Strong convergence of inertial extragradient algorithms for solving variational inequalities and fixed point problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Fixed Point Theory</i>, 23(2): 707–728.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TLQ-FPT2022.pdf\"\n     onclick=\"log_download('tan-liu-qin-strongconvergenceofinertialextragradientalgorithmsforsolvingvariationalinequalitiesandfixedpointproblems-2022', 'https://bingtan.me/files/paper/TLQ-FPT2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Strong convergence of inertial extragradient algorithms for solving variational inequalities and fixed point problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.24193/fpt-ro.2022.2.17\"\n     onclick=\"log_download('tan-liu-qin-strongconvergenceofinertialextragradientalgorithmsforsolvingvariationalinequalitiesandfixedpointproblems-2022', 'http://doi.org/10.24193/fpt-ro.2022.2.17', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-liu-qin-strongconvergenceofinertialextragradientalgorithmsforsolvingvariationalinequalitiesandfixedpointproblems-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-liu-qin-strongconvergenceofinertialextragradientalgorithmsforsolvingvariationalinequalitiesandfixedpointproblems-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TLQ_FPT22,\nauthor={Tan, Bing and Liu, Liya and Qin, Xiaolong},\ntitle={Strong convergence of inertial extragradient algorithms for solving variational inequalities and fixed point problems},\njournal={Fixed Point Theory},\nyear={2022},\nvolume={23},\nnumber={2},\npages={707--728},\ndoi={10.24193/fpt-ro.2022.2.17},\nurl={https://bingtan.me/files/paper/TLQ-FPT2022.pdf},\nabstract={This paper investigates two inertial extragradient algorithms for seeking a common solution to a variational inequality problem involving a monotone and Lipschitz continuous mapping and a fixed point problem with a demicontractive mapping in real Hilbert spaces. Our algorithms need to calculate the projection on the feasible set only once in each iteration. Moreover, they can work well without the prior information of the Lipschitz constant of the operator and do not contain any linesearch process. Strong convergence theorems of the suggested algorithms are established under suitable conditions. Some experiments are presented to illustrate the numerical efficiency of the suggested algorithms and compare them with some existing ones.},\nkeywords={Variational inequality problem, Fixed point problem, Subgradient extragradient method, Tseng&#x27;s extragradient method, Inertial method, Demicontractive mapping},\nabbrev_source_title={Fixed Point Theory},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This paper investigates two inertial extragradient algorithms for seeking a common solution to a variational inequality problem involving a monotone and Lipschitz continuous mapping and a fixed point problem with a demicontractive mapping in real Hilbert spaces. Our algorithms need to calculate the projection on the feasible set only once in each iteration. Moreover, they can work well without the prior information of the Lipschitz constant of the operator and do not contain any linesearch process. Strong convergence theorems of the suggested algorithms are established under suitable conditions. Some experiments are presented to illustrate the numerical efficiency of the suggested algorithms and compare them with some existing ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-li-modifiedinertialprojectionandcontractionalgorithmswithnonmonotonicstepsizesforsolvingvariationalinequalitiesandtheirapplications-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Modified inertial projection and contraction algorithms with non-monotonic step sizes for solving variational inequalities and their applications.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Optimization</i>, doi:10.1080/02331934.2022.2123705.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TL-OPT2022.pdf\"\n     onclick=\"log_download('tan-li-modifiedinertialprojectionandcontractionalgorithmswithnonmonotonicstepsizesforsolvingvariationalinequalitiesandtheirapplications-2022', 'https://bingtan.me/files/paper/TL-OPT2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Modified inertial projection and contraction algorithms with non-monotonic step sizes for solving variational inequalities and their applications [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1080/02331934.2022.2123705\"\n     onclick=\"log_download('tan-li-modifiedinertialprojectionandcontractionalgorithmswithnonmonotonicstepsizesforsolvingvariationalinequalitiesandtheirapplications-2022', 'http://doi.org/10.1080/02331934.2022.2123705', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-li-modifiedinertialprojectionandcontractionalgorithmswithnonmonotonicstepsizesforsolvingvariationalinequalitiesandtheirapplications-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-li-modifiedinertialprojectionandcontractionalgorithmswithnonmonotonicstepsizesforsolvingvariationalinequalitiesandtheirapplications-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TL_OPT22,\nauthor={Tan, Bing and Li, Songxiao},\ntitle={Modified inertial projection and contraction algorithms with non-monotonic step sizes for solving variational inequalities and their applications},\njournal={Optimization},\nyear={2022},\nvolume={doi:10.1080/02331934.2022.2123705},\ndoi={10.1080/02331934.2022.2123705},\nurl={https://bingtan.me/files/paper/TL-OPT2022.pdf},\nabstract={We present two adaptive inertial projection and contraction algorithms to discover the minimum-norm solutions of pseudomonotone variational inequality problems in real Hilbert spaces. The suggested algorithms employ two different step sizes in each iteration and use a non-monotone step size criterion without any line search allowing them to work adaptively. The strong convergence of the iterative sequences formed by the proposed algorithms is established under some mild conditions. Several numerical experiments occurring in finite- and infinite-dimensional Hilbert spaces and applications to optimal control problems as well as signal processing problems are given. Performance profiles are used to verify the computational efficiency and advantages of the proposed algorithms with respect to some known ones.},\nkeywords={Variational inequality problem,  Inertial method,  Projection and contraction method,  Subgradient extragradient method, Pseudomonotone operator, Optimal control problem, Signal processing problem, Strong convergence},\nabbrev_source_title={Optimization},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We present two adaptive inertial projection and contraction algorithms to discover the minimum-norm solutions of pseudomonotone variational inequality problems in real Hilbert spaces. The suggested algorithms employ two different step sizes in each iteration and use a non-monotone step size criterion without any line search allowing them to work adaptively. The strong convergence of the iterative sequences formed by the proposed algorithms is established under some mild conditions. Several numerical experiments occurring in finite- and infinite-dimensional Hilbert spaces and applications to optimal control problems as well as signal processing problems are given. Performance profiles are used to verify the computational efficiency and advantages of the proposed algorithms with respect to some known ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-li-revisitingprojectionandcontractionalgorithmsforsolvingvariationalinequalitiesandapplications-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Revisiting projection and contraction algorithms for solving variational inequalities and applications.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Applied Set-Valued Analysis and Optimization</i>, 4(2): 167–183.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TL-ASVAO2022.pdf\"\n     onclick=\"log_download('tan-li-revisitingprojectionandcontractionalgorithmsforsolvingvariationalinequalitiesandapplications-2022', 'https://bingtan.me/files/paper/TL-ASVAO2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Revisiting projection and contraction algorithms for solving variational inequalities and applications [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.23952/asvao.4.2022.2.03\"\n     onclick=\"log_download('tan-li-revisitingprojectionandcontractionalgorithmsforsolvingvariationalinequalitiesandapplications-2022', 'http://doi.org/10.23952/asvao.4.2022.2.03', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-li-revisitingprojectionandcontractionalgorithmsforsolvingvariationalinequalitiesandapplications-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-li-revisitingprojectionandcontractionalgorithmsforsolvingvariationalinequalitiesandapplications-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TL_ASVAO22,\nauthor={Tan, Bing and Li, Songxiao},\ntitle={Revisiting projection and contraction algorithms for solving variational inequalities and applications},\njournal={Applied Set-Valued Analysis and Optimization},\nyear={2022},\nvolume={4},\nnumber={2},\npages={167--183},\ndoi={10.23952/asvao.4.2022.2.03},\nurl={https://bingtan.me/files/paper/TL-ASVAO2022.pdf},\nabstract={We provide two novel projection and contraction algorithms to find the minimum-norm solution of the variational inequality problem with a pseudo monotone and non-Lipschitz continuous operator in a real Hilbert space. Our algorithms can work adaptively without requiring the prior information of the Lipschitz constant of the operator. Strong convergence theorems for the suggested iterative algorithms are established under suitable conditions. Some numerical experiments are discussed to demonstrate the computational efficiency of the proposed algorithms in comparison with several existing ones.},\nkeywords={Variational inequality problem, Subgradient extragradient method, Projection and contraction method, Inertial method, Pseudomonotone operator},\nabbrev_source_title={Appl. Set-Valued Anal. Optim.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We provide two novel projection and contraction algorithms to find the minimum-norm solution of the variational inequality problem with a pseudo monotone and non-Lipschitz continuous operator in a real Hilbert space. Our algorithms can work adaptively without requiring the prior information of the Lipschitz constant of the operator. Strong convergence theorems for the suggested iterative algorithms are established under suitable conditions. Some numerical experiments are discussed to demonstrate the computational efficiency of the proposed algorithms in comparison with several existing ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-zhou-li-viscositytypeinertialextragradientalgorithmsforsolvingvariationalinequalityproblemsandfixedpointproblems-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Zhou, Z.;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Viscosity-type inertial extragradient algorithms for solving variational inequality problems and fixed point problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Applied Mathematics and Computing</i>, 68(2): 1387–1411.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TZL-JAMC2022.pdf\"\n     onclick=\"log_download('tan-zhou-li-viscositytypeinertialextragradientalgorithmsforsolvingvariationalinequalityproblemsandfixedpointproblems-2022', 'https://bingtan.me/files/paper/TZL-JAMC2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Viscosity-type inertial extragradient algorithms for solving variational inequality problems and fixed point problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s12190-021-01576-z\"\n     onclick=\"log_download('tan-zhou-li-viscositytypeinertialextragradientalgorithmsforsolvingvariationalinequalityproblemsandfixedpointproblems-2022', 'http://doi.org/10.1007/s12190-021-01576-z', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-zhou-li-viscositytypeinertialextragradientalgorithmsforsolvingvariationalinequalityproblemsandfixedpointproblems-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-zhou-li-viscositytypeinertialextragradientalgorithmsforsolvingvariationalinequalityproblemsandfixedpointproblems-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TZL_JAMC22,\nauthor={Tan, Bing and Zhou, Zheng and Li, Songxiao},\ntitle={Viscosity-type inertial extragradient algorithms for solving variational inequality problems and fixed point problems},\njournal={Journal of Applied Mathematics and Computing},\nyear={2022},\nvolume={68},\nnumber={2},\npages={1387--1411},\ndoi={10.1007/s12190-021-01576-z},\nurl={https://bingtan.me/files/paper/TZL-JAMC2022.pdf},\nabstract={The paper presents two inertial viscosity-type extragradient algorithms for finding a common solution of the variational inequality problem involving a monotone and Lipschitz continuous operator and of the fixed point problem with a demicontractive mapping in real Hilbert spaces. Our algorithms use a simple step size rule which is generated by some calculations at each iteration. Two strong convergence theorems are obtained without the prior knowledge of the Lipschitz constant of the operator. The numerical behaviors of the proposed algorithms in some numerical experiments are reported and compared with previously known ones.},\nkeywords={Fixed point problem,  Inertial method,  Subgradient extragradient method,  Tseng&#x27;s extragradient method,  Variational inequality problem},\nabbrev_source_title={J. Appl. Math. Comput.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  The paper presents two inertial viscosity-type extragradient algorithms for finding a common solution of the variational inequality problem involving a monotone and Lipschitz continuous operator and of the fixed point problem with a demicontractive mapping in real Hilbert spaces. Our algorithms use a simple step size rule which is generated by some calculations at each iteration. Two strong convergence theorems are obtained without the prior knowledge of the Lipschitz constant of the operator. The numerical behaviors of the proposed algorithms in some numerical experiments are reported and compared with previously known ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-li-cho-revisitinginertialsubgradientextragradientalgorithmsforsolvingbilevelvariationalinequalityproblems-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Li, S.;  and Cho, S. Y.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Revisiting inertial subgradient extragradient algorithms for solving bilevel variational inequality problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Applied and Numerical Optimization</i>, 4(3): 425–444.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TLC-JANO2022.pdf\"\n     onclick=\"log_download('tan-li-cho-revisitinginertialsubgradientextragradientalgorithmsforsolvingbilevelvariationalinequalityproblems-2022', 'https://bingtan.me/files/paper/TLC-JANO2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Revisiting inertial subgradient extragradient algorithms for solving bilevel variational inequality problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.23952/jano.4.2022.3.08\"\n     onclick=\"log_download('tan-li-cho-revisitinginertialsubgradientextragradientalgorithmsforsolvingbilevelvariationalinequalityproblems-2022', 'http://doi.org/10.23952/jano.4.2022.3.08', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-li-cho-revisitinginertialsubgradientextragradientalgorithmsforsolvingbilevelvariationalinequalityproblems-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>1 download</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-li-cho-revisitinginertialsubgradientextragradientalgorithmsforsolvingbilevelvariationalinequalityproblems-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TLC_JANO22,\nauthor={Tan, Bing and Li, Songxiao and Cho, Sun Y.},\ntitle={Revisiting inertial subgradient extragradient algorithms for solving bilevel variational inequality problems},\njournal={Journal of Applied and Numerical Optimization},\nyear={2022},\nvolume={4},\nnumber={3},\npages={425--444},\ndoi={10.23952/jano.4.2022.3.08},\nurl={https://bingtan.me/files/paper/TLC-JANO2022.pdf},\nabstract={In this paper, four modified subgradient extragradient algorithms are proposed for solving bilevel pseudomonotone variational inequality problems in real Hilbert spaces. The proposed algorithms can work adaptively without the prior knowledge of the Lipschitz constant of the pseudomonotone mapping. Strong convergence theorems for the suggested algorithms are established under suitable and mild conditions. Finally, some numerical experiments and applications are performed to verify the efficiency of the proposed algorithms with respect to some previously known ones.},\nkeywords={Inertial method, Pseudomonotone operator, Subgradient extragradient method, Bilevel variational inequality problem},\nabbrev_source_title={J. Appl. Numer. Optim.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, four modified subgradient extragradient algorithms are proposed for solving bilevel pseudomonotone variational inequality problems in real Hilbert spaces. The proposed algorithms can work adaptively without the prior knowledge of the Lipschitz constant of the pseudomonotone mapping. Strong convergence theorems for the suggested algorithms are established under suitable and mild conditions. Finally, some numerical experiments and applications are performed to verify the efficiency of the proposed algorithms with respect to some previously known ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-cho-yao-acceleratedinertialsubgradientextragradientalgorithmswithnonmonotonicstepsizesforequilibriumproblemsandfixedpointproblems-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Cho, S. Y.;  and Yao, J. C.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Accelerated inertial subgradient extragradient algorithms with non-monotonic step sizes for equilibrium problems and fixed point problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Nonlinear and Variational Analysis</i>, 6(1): 89–122.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TCY-JNVA2022.pdf\"\n     onclick=\"log_download('tan-cho-yao-acceleratedinertialsubgradientextragradientalgorithmswithnonmonotonicstepsizesforequilibriumproblemsandfixedpointproblems-2022', 'https://bingtan.me/files/paper/TCY-JNVA2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Accelerated inertial subgradient extragradient algorithms with non-monotonic step sizes for equilibrium problems and fixed point problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.23952/jnva.6.2022.1.06\"\n     onclick=\"log_download('tan-cho-yao-acceleratedinertialsubgradientextragradientalgorithmswithnonmonotonicstepsizesforequilibriumproblemsandfixedpointproblems-2022', 'http://doi.org/10.23952/jnva.6.2022.1.06', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-cho-yao-acceleratedinertialsubgradientextragradientalgorithmswithnonmonotonicstepsizesforequilibriumproblemsandfixedpointproblems-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-cho-yao-acceleratedinertialsubgradientextragradientalgorithmswithnonmonotonicstepsizesforequilibriumproblemsandfixedpointproblems-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TCY_JNVA22,\nauthor={Tan, Bing and Cho, Sun Y. and Yao, Jen C.},\ntitle={Accelerated inertial subgradient extragradient algorithms with non-monotonic step sizes for equilibrium problems and fixed point problems},\njournal={Journal of Nonlinear and Variational Analysis},\nyear={2022},\nvolume={6},\nnumber={1},\npages={89--122},\ndoi={10.23952/jnva.6.2022.1.06},\nurl={https://bingtan.me/files/paper/TCY-JNVA2022.pdf},\nabstract={This paper introduces several new accelerated subgradient extragradient methods with inertial effects for approximating a solution of a pseudomonotone equilibrium problem and a fixed point problem involving a quasi-nonexpansive mapping or a demicontractive mapping in real Hilbert spaces. The proposed algorithms use an adaptive non-monotonic step size criterion that does not include any Armijo line search process. Strong convergence theorems of the suggested iterative algorithms are established without the prior knowledge of the Lipschitz constants of the bifunction. Moreover, $R$-linear convergence is guaranteed under the assumption that the bifunction satisfies strong pseudomonotonicity. Applications to variational inequality problems are also considered. Finally, some numerical examples and applications, which demonstrate the advantages and efficiency of the proposed algorithms, are given.},\nkeywords={Equilibrium problem,  Fixed point problem,  Inertial method,  Pseudomonotone bifunction,  Subgradient extragradient method},\nabbrev_source_title={J. Nonlinear Var. Anal.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This paper introduces several new accelerated subgradient extragradient methods with inertial effects for approximating a solution of a pseudomonotone equilibrium problem and a fixed point problem involving a quasi-nonexpansive mapping or a demicontractive mapping in real Hilbert spaces. The proposed algorithms use an adaptive non-monotonic step size criterion that does not include any Armijo line search process. Strong convergence theorems of the suggested iterative algorithms are established without the prior knowledge of the Lipschitz constants of the bifunction. Moreover, $R$-linear convergence is guaranteed under the assumption that the bifunction satisfies strong pseudomonotonicity. Applications to variational inequality problems are also considered. Finally, some numerical examples and applications, which demonstrate the advantages and efficiency of the proposed algorithms, are given.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-cho-twoadaptivemodifiedsubgradientextragradientmethodsforbilevelpseudomonotonevariationalinequalitieswithapplications-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Cho, S. Y.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Two adaptive modified subgradient extragradient methods for bilevel pseudomonotone variational inequalities with applications.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Communications in Nonlinear Science and Numerical Simulation</i>, 107: 106160.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TC-CNSNS2022.pdf\"\n     onclick=\"log_download('tan-cho-twoadaptivemodifiedsubgradientextragradientmethodsforbilevelpseudomonotonevariationalinequalitieswithapplications-2022', 'https://bingtan.me/files/paper/TC-CNSNS2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Two adaptive modified subgradient extragradient methods for bilevel pseudomonotone variational inequalities with applications [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1016/j.cnsns.2021.106160\"\n     onclick=\"log_download('tan-cho-twoadaptivemodifiedsubgradientextragradientmethodsforbilevelpseudomonotonevariationalinequalitieswithapplications-2022', 'http://doi.org/10.1016/j.cnsns.2021.106160', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-cho-twoadaptivemodifiedsubgradientextragradientmethodsforbilevelpseudomonotonevariationalinequalitieswithapplications-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-cho-twoadaptivemodifiedsubgradientextragradientmethodsforbilevelpseudomonotonevariationalinequalitieswithapplications-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TC_CNSNS22,\nauthor={Tan, Bing and Cho, Sun Y.},\ntitle={Two adaptive modified subgradient extragradient methods for bilevel pseudomonotone variational inequalities with applications},\njournal={Communications in Nonlinear Science and Numerical Simulation},\nyear={2022},\nvolume={107},\ndoi={10.1016/j.cnsns.2021.106160},\npages={106160},\nurl={https://bingtan.me/files/paper/TC-CNSNS2022.pdf},\nabstract={We consider the bilevel variational inequality problem with a pseudomonotone operator in real Hilbert spaces and investigate two modified subgradient extragradient methods with inertial terms. Our first scheme requires the operator to be Lipschitz continuous (the Lipschitz constant does not need to be known) while the second one only requires it to be uniformly continuous. The proposed methods employ two adaptive stepsizes making them work without the prior knowledge of the Lipschitz constant of the mapping. The strong convergence properties of the iterative sequences generated by the proposed algorithms are obtained under mild conditions. Some numerical tests and applications are given to demonstrate the advantages and efficiency of the stated schemes over previously known ones.},\nkeywords={Adaptive stepsize,  Bilevel variational inequality problem,  Extragradient method,  Inertial method,  Pseudomonotone operator},\nabbrev_source_title={Comm. Nonlinear Sci. Numer. Simul.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We consider the bilevel variational inequality problem with a pseudomonotone operator in real Hilbert spaces and investigate two modified subgradient extragradient methods with inertial terms. Our first scheme requires the operator to be Lipschitz continuous (the Lipschitz constant does not need to be known) while the second one only requires it to be uniformly continuous. The proposed methods employ two adaptive stepsizes making them work without the prior knowledge of the Lipschitz constant of the mapping. The strong convergence properties of the iterative sequences generated by the proposed algorithms are obtained under mild conditions. Some numerical tests and applications are given to demonstrate the advantages and efficiency of the stated schemes over previously known ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-cho-twoprojectionbasedmethodsforbilevelpseudomonotonevariationalinequalitiesinvolvingnonlipschitzoperators-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Cho, S. Y.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Two projection-based methods for bilevel pseudomonotone variational inequalities involving non-Lipschitz operators.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas</i>, 116(2): 64.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TC-RACSAM2022.pdf\"\n     onclick=\"log_download('tan-cho-twoprojectionbasedmethodsforbilevelpseudomonotonevariationalinequalitiesinvolvingnonlipschitzoperators-2022', 'https://bingtan.me/files/paper/TC-RACSAM2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Two projection-based methods for bilevel pseudomonotone variational inequalities involving non-Lipschitz operators [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s13398-021-01205-1\"\n     onclick=\"log_download('tan-cho-twoprojectionbasedmethodsforbilevelpseudomonotonevariationalinequalitiesinvolvingnonlipschitzoperators-2022', 'http://doi.org/10.1007/s13398-021-01205-1', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-cho-twoprojectionbasedmethodsforbilevelpseudomonotonevariationalinequalitiesinvolvingnonlipschitzoperators-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-cho-twoprojectionbasedmethodsforbilevelpseudomonotonevariationalinequalitiesinvolvingnonlipschitzoperators-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TC_RCSM22,\nauthor={Tan, Bing and Cho, Sun Y.},\ntitle={Two projection-based methods for bilevel pseudomonotone variational inequalities involving non-Lipschitz operators},\njournal={Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas},\nyear={2022},\nvolume={116},\nnumber={2},\ndoi={10.1007/s13398-021-01205-1},\npages={64},\nurl={https://bingtan.me/files/paper/TC-RACSAM2022.pdf},\nabstract={In this paper, we propose two new iterative algorithms to discover solutions of bilevel pseudomonotone variational inequalities with non-Lipschitz continuous operators in real Hilbert spaces. Our proposed algorithms need to compute the projection on the feasible set only once in each iteration although they employ Armijo line search methods. Strong convergence theorems of the suggested algorithms are established under suitable and weaker conditions. Some numerical experiments and applications are given to demonstrate the performance of the offered algorithms compared to some known ones.},\nkeywords={Armijo stepsize,  Bilevel variational inequality problem,  Inertial method,  Non-Lipschitz operator,  Pseudomonotone operator},\nabbrev_source_title={Rev. R. Acad. Cienc. Exactas F{\\&#x27; i}s. Nat. Ser. A Mat. RACSAM},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we propose two new iterative algorithms to discover solutions of bilevel pseudomonotone variational inequalities with non-Lipschitz continuous operators in real Hilbert spaces. Our proposed algorithms need to compute the projection on the feasible set only once in each iteration although they employ Armijo line search methods. Strong convergence theorems of the suggested algorithms are established under suitable and weaker conditions. Some numerical experiments and applications are given to demonstrate the performance of the offered algorithms compared to some known ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-cho-strongconvergenceofinertialforwardbackwardmethodsforsolvingmonotoneinclusions-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Cho, S. Y.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Strong convergence of inertial forward-backward methods for solving monotone inclusions.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Applicable Analysis</i>, 101(15): 5386–5414.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><span style=\"color: red\">(ESI Highly Cited Paper)</span></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TC-AA2022.pdf\"\n     onclick=\"log_download('tan-cho-strongconvergenceofinertialforwardbackwardmethodsforsolvingmonotoneinclusions-2022', 'https://bingtan.me/files/paper/TC-AA2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Strong convergence of inertial forward-backward methods for solving monotone inclusions [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1080/00036811.2021.1892080\"\n     onclick=\"log_download('tan-cho-strongconvergenceofinertialforwardbackwardmethodsforsolvingmonotoneinclusions-2022', 'http://doi.org/10.1080/00036811.2021.1892080', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-cho-strongconvergenceofinertialforwardbackwardmethodsforsolvingmonotoneinclusions-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-cho-strongconvergenceofinertialforwardbackwardmethodsforsolvingmonotoneinclusions-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TC_AA22,\nauthor={Tan, Bing and Cho, Sun Y.},\ntitle={Strong convergence of inertial forward-backward methods for solving monotone inclusions},\njournal={Applicable Analysis},\nyear={2022},\nvolume={101},\nnumber={15},\npages={5386--5414},\ndoi={10.1080/00036811.2021.1892080},\nurl={https://bingtan.me/files/paper/TC-AA2022.pdf},\nabstract={The paper presents four modifications of the inertial forward–backward splitting method for monotone inclusion problems in the framework of real Hilbert spaces. The advantages of our iterative schemes are that the single-valued operator is Lipschitz continuous monotone rather than cocoercive and the Lipschitz constant does not require to be known. The strong convergence of the suggested approaches is obtained under some standard and mild conditions. Finally, several numerical experiments in finite- and infinite-dimensional spaces are proposed to demonstrate the advantages of our algorithms over the existing related ones.},\nkeywords={Inclusion problem,  Inertial forward–backward method,  Projection and contraction method,  Tseng&#x27;s extragradient method,  Viscosity method, Signal processing problem},\nabbrev_source_title={Appl. Anal.},\nbibbase_note={&lt;span style=&quot;color: red&quot;&gt;(ESI Highly Cited Paper)&lt;/span&gt;},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  The paper presents four modifications of the inertial forward–backward splitting method for monotone inclusion problems in the framework of real Hilbert spaces. The advantages of our iterative schemes are that the single-valued operator is Lipschitz continuous monotone rather than cocoercive and the Lipschitz constant does not require to be known. The strong convergence of the suggested approaches is obtained under some standard and mild conditions. Finally, several numerical experiments in finite- and infinite-dimensional spaces are proposed to demonstrate the advantages of our algorithms over the existing related ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-cho-inertialextragradientalgorithmswithnonmonotonestepsizesforpseudomonotonevariationalinequalitiesandapplications-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Cho, S. Y.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Inertial extragradient algorithms with non-monotone stepsizes for pseudomonotone variational inequalities and applications.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Computational and Applied Mathematics</i>, 41(3): 121.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TC-COAM2022.pdf\"\n     onclick=\"log_download('tan-cho-inertialextragradientalgorithmswithnonmonotonestepsizesforpseudomonotonevariationalinequalitiesandapplications-2022', 'https://bingtan.me/files/paper/TC-COAM2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Inertial extragradient algorithms with non-monotone stepsizes for pseudomonotone variational inequalities and applications [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s40314-022-01819-0\"\n     onclick=\"log_download('tan-cho-inertialextragradientalgorithmswithnonmonotonestepsizesforpseudomonotonevariationalinequalitiesandapplications-2022', 'http://doi.org/10.1007/s40314-022-01819-0', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-cho-inertialextragradientalgorithmswithnonmonotonestepsizesforpseudomonotonevariationalinequalitiesandapplications-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-cho-inertialextragradientalgorithmswithnonmonotonestepsizesforpseudomonotonevariationalinequalitiesandapplications-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TC_COAM22,\nauthor={Tan, Bing and Cho, Sun Y.},\ntitle={Inertial extragradient algorithms with non-monotone stepsizes for pseudomonotone variational inequalities and applications},\njournal={Computational and Applied Mathematics},\nyear={2022},\nvolume={41},\nnumber={3},\ndoi={10.1007/s40314-022-01819-0},\npages={121},\nurl={https://bingtan.me/files/paper/TC-COAM2022.pdf},\nabstract={The goal of this paper is to construct several fast iterative algorithms for solving pseudomonotone variational inequalities in real Hilbert spaces. We introduce two extragradient algorithms with inertial terms and give a strong convergence analysis under suitable assumptions. The suggested algorithms need to compute the projection on the feasible set only once in each iteration and can update the step size adaptively without any line search condition. Some numerical experiments and applications are implemented to illustrate the advantages and efficiency of the suggested algorithms over the related known methods.},\nkeywords={Inertial method,  Pseudomonotone operator,  Subgradient extragradient method,  Tseng&#x27;s extragradient method,  Variational inequality problem},\nabbrev_source_title={Comput. Appl. Math.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  The goal of this paper is to construct several fast iterative algorithms for solving pseudomonotone variational inequalities in real Hilbert spaces. We introduce two extragradient algorithms with inertial terms and give a strong convergence analysis under suitable assumptions. The suggested algorithms need to compute the projection on the feasible set only once in each iteration and can update the step size adaptively without any line search condition. Some numerical experiments and applications are implemented to illustrate the advantages and efficiency of the suggested algorithms over the related known methods.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-cho-twonewprojectionalgorithmsforvariationalinequalitiesinhilbertspaces-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Cho, S. Y.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Two new projection algorithms for variational inequalities in Hilbert spaces.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Nonlinear and Convex Analysis</i>, 23(11): 2523–2534.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TC-JNCA2022.pdf\"\n     onclick=\"log_download('tan-cho-twonewprojectionalgorithmsforvariationalinequalitiesinhilbertspaces-2022', 'https://bingtan.me/files/paper/TC-JNCA2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Two new projection algorithms for variational inequalities in Hilbert spaces [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-cho-twonewprojectionalgorithmsforvariationalinequalitiesinhilbertspaces-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-cho-twonewprojectionalgorithmsforvariationalinequalitiesinhilbertspaces-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TC_JNCA22,\nauthor={Tan, Bing and Cho, Sun Y.},\ntitle={Two new projection algorithms for variational inequalities in Hilbert spaces},\njournal={Journal of Nonlinear and Convex Analysis},\nyear={2022},\nvolume={23},\nnumber={11},\npages={2523--2534},\nurl={https://bingtan.me/files/paper/TC-JNCA2022.pdf},\nabstract={In this paper, two new projection-type algorithms are introduced for solving pseudomonotone variational inequalities in real Hilbert spaces. The proposed methods use two non-monotonic step sizes allowing them to work adaptively without the prior information of the Lipschitz constant of the operator. Strong convergence theorems for the proposed methods are established under suitable conditions. A fundamental numerical example is given to verify the efficiency of the suggested methods in comparison with some known ones.},\nkeywords={Inertial method, Pseudomonotone operator,  Variational inequality problem, Projection method},\nabbrev_source_title={J. Nonlinear Convex Anal.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, two new projection-type algorithms are introduced for solving pseudomonotone variational inequalities in real Hilbert spaces. The proposed methods use two non-monotonic step sizes allowing them to work adaptively without the prior information of the Lipschitz constant of the operator. Strong convergence theorems for the proposed methods are established under suitable conditions. A fundamental numerical example is given to verify the efficiency of the suggested methods in comparison with some known ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"zhou-tan-li-adaptivehybridsteepestdescentalgorithmsinvolvinganinertialextrapolationtermforsplitmonotonevariationalinclusionproblems-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Zhou, Z.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Adaptive hybrid steepest descent algorithms involving an inertial extrapolation term for split monotone variational inclusion problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Mathematical Methods in the Applied Sciences</i>, 45(15): 8835–8853.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/ZTL-MMAS2022.pdf\"\n     onclick=\"log_download('zhou-tan-li-adaptivehybridsteepestdescentalgorithmsinvolvinganinertialextrapolationtermforsplitmonotonevariationalinclusionproblems-2022', 'https://bingtan.me/files/paper/ZTL-MMAS2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Adaptive hybrid steepest descent algorithms involving an inertial extrapolation term for split monotone variational inclusion problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1002/mma.7931\"\n     onclick=\"log_download('zhou-tan-li-adaptivehybridsteepestdescentalgorithmsinvolvinganinertialextrapolationtermforsplitmonotonevariationalinclusionproblems-2022', 'http://doi.org/10.1002/mma.7931', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/zhou-tan-li-adaptivehybridsteepestdescentalgorithmsinvolvinganinertialextrapolationtermforsplitmonotonevariationalinclusionproblems-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>1 download</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('zhou-tan-li-adaptivehybridsteepestdescentalgorithmsinvolvinganinertialextrapolationtermforsplitmonotonevariationalinclusionproblems-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{ZTL_MMAS22,\nauthor={Zhou, Zheng and Tan, Bing and Li, Songxiao},\ntitle={Adaptive hybrid steepest descent algorithms involving an inertial extrapolation term for split monotone variational inclusion problems},\njournal={Mathematical Methods in the Applied Sciences},\nyear={2022},\nvolume={45},\nnumber={15},\npages={8835--8853},\ndoi={10.1002/mma.7931},\nurl={https://bingtan.me/files/paper/ZTL-MMAS2022.pdf},\nabstract={In this paper, we discuss the split monotone variational inclusion problem and propose two new inertial algorithms in infinite-dimensional Hilbert spaces. The iterative sequence by the proposed algorithms converges strongly to the solution of a certain variational inequality with the help of the hybrid steepest descent method. Furthermore, an adaptive step size criterion is considered in suggested algorithms to avoid the difficulty of calculating the operator norm. Meanwhile, our results are also applied to several other types of split problems. Finally, some numerical experiments show that our algorithms are realistic and summarize the known results.},\nkeywords={Adaptive stepsize,  Hybrid steepest descent method,  Inertial method,  Signal processing problem,  Strong convergence},\nabbrev_source_title={Math. Methods Appl. Sci.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we discuss the split monotone variational inclusion problem and propose two new inertial algorithms in infinite-dimensional Hilbert spaces. The iterative sequence by the proposed algorithms converges strongly to the solution of a certain variational inequality with the help of the hybrid steepest descent method. Furthermore, an adaptive step size criterion is considered in suggested algorithms to avoid the difficulty of calculating the operator norm. Meanwhile, our results are also applied to several other types of split problems. Finally, some numerical experiments show that our algorithms are realistic and summarize the known results.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"zhou-tan-cho-alternatedinertialsubgradientextragradientmethodsforsolvingvariationalinequalities-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Zhou, Z.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Cho, S. Y.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Alternated inertial subgradient extragradient methods for solving variational inequalities.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Nonlinear and Convex Analysis</i>, 23(11): 2593–2604.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/ZTC-JNCA2022.pdf\"\n     onclick=\"log_download('zhou-tan-cho-alternatedinertialsubgradientextragradientmethodsforsolvingvariationalinequalities-2022', 'https://bingtan.me/files/paper/ZTC-JNCA2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Alternated inertial subgradient extragradient methods for solving variational inequalities [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/zhou-tan-cho-alternatedinertialsubgradientextragradientmethodsforsolvingvariationalinequalities-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('zhou-tan-cho-alternatedinertialsubgradientextragradientmethodsforsolvingvariationalinequalities-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{ZTC_JNCA22,\nauthor={Zhou, Zheng and Tan, Bing and Cho, Sun Y.},\ntitle={Alternated inertial subgradient extragradient methods for solving variational inequalities},\njournal={Journal of Nonlinear and Convex Analysis},\nyear={2022},\nvolume={23},\nnumber={11},\npages={2593--2604},\nurl={https://bingtan.me/files/paper/ZTC-JNCA2022.pdf},\nabstract={The goal of this paper is to study some iterative algorithms for solving a pseudomonotone variational inequality in Hilbert spaces. The iterative algorithms presented in this paper are based on the alternated inertial method and the subgradient extragradient method. Weak convergence of the algorithms is established by the adaptive stepsize criterion in Hilbert spaces.},\nkeywords={Alternated inertial method, Pseudomonotone operator,  Variational inequality problem, Subgradient extragradient method},\nabbrev_source_title={J. Nonlinear Convex Anal.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  The goal of this paper is to study some iterative algorithms for solving a pseudomonotone variational inequality in Hilbert spaces. The iterative algorithms presented in this paper are based on the alternated inertial method and the subgradient extragradient method. Weak convergence of the algorithms is established by the adaptive stepsize criterion in Hilbert spaces.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"zhou-tan-li-twoselfadaptiveinertialprojectionalgorithmsforsolvingsplitvariationalinclusionproblems-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Zhou, Z.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Two self-adaptive inertial projection algorithms for solving split variational inclusion problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>AIMS Mathematics</i>, 7(4): 4960–4973.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/ZTL-AIMS2022.pdf\"\n     onclick=\"log_download('zhou-tan-li-twoselfadaptiveinertialprojectionalgorithmsforsolvingsplitvariationalinclusionproblems-2022', 'https://bingtan.me/files/paper/ZTL-AIMS2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Two self-adaptive inertial projection algorithms for solving split variational inclusion problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.3934/math.2022276\"\n     onclick=\"log_download('zhou-tan-li-twoselfadaptiveinertialprojectionalgorithmsforsolvingsplitvariationalinclusionproblems-2022', 'http://doi.org/10.3934/math.2022276', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/zhou-tan-li-twoselfadaptiveinertialprojectionalgorithmsforsolvingsplitvariationalinclusionproblems-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('zhou-tan-li-twoselfadaptiveinertialprojectionalgorithmsforsolvingsplitvariationalinclusionproblems-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{ZTL_AIMS22,\nauthor={Zhou, Zheng and Tan, Bing and Li, Songxiao},\ntitle={Two self-adaptive inertial projection algorithms for solving split variational inclusion problems},\njournal={AIMS Mathematics},\nyear={2022},\nvolume={7},\nnumber={4},\npages={4960--4973},\ndoi={10.3934/math.2022276},\nurl={https://bingtan.me/files/paper/ZTL-AIMS2022.pdf},\nabstract={This paper is to analyze the approximation solution of a split variational inclusion problem in the framework of Hilbert spaces. For this purpose, inertial hybrid and shrinking projection algorithms are proposed under the effect of a self-adaptive stepsize which does not require information of the norms of the given operators. The strong convergence properties of the proposed algorithms are obtained under mild constraints. Finally, a numerical experiment is given to illustrate the performance of proposed methods and to compare our algorithms with an existing algorithm.},\nkeywords={Inertial method,  Adaptive stepsize,  Split variational inclusion problem},\nabbrev_source_title={AIMS Math.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This paper is to analyze the approximation solution of a split variational inclusion problem in the framework of Hilbert spaces. For this purpose, inertial hybrid and shrinking projection algorithms are proposed under the effect of a self-adaptive stepsize which does not require information of the norms of the given operators. The strong convergence properties of the proposed algorithms are obtained under mild constraints. Finally, a numerical experiment is given to illustrate the performance of proposed methods and to compare our algorithms with an existing algorithm.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"fan-qin-tan-tsengsextragradientalgorithmforpseudomonotonevariationalinequalitiesonhadamardmanifolds-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Fan, J.; Qin, X.;  and <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Tseng's extragradient algorithm for pseudomonotone variational inequalities on Hadamard manifolds.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Applicable Analysis</i>, 101(6): 2372–2385.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/FQT-AA2022.pdf\"\n     onclick=\"log_download('fan-qin-tan-tsengsextragradientalgorithmforpseudomonotonevariationalinequalitiesonhadamardmanifolds-2022', 'https://bingtan.me/files/paper/FQT-AA2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Tseng&#x27;s extragradient algorithm for pseudomonotone variational inequalities on Hadamard manifolds [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1080/00036811.2020.1807012\"\n     onclick=\"log_download('fan-qin-tan-tsengsextragradientalgorithmforpseudomonotonevariationalinequalitiesonhadamardmanifolds-2022', 'http://doi.org/10.1080/00036811.2020.1807012', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/fan-qin-tan-tsengsextragradientalgorithmforpseudomonotonevariationalinequalitiesonhadamardmanifolds-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('fan-qin-tan-tsengsextragradientalgorithmforpseudomonotonevariationalinequalitiesonhadamardmanifolds-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{FQT_AA22,\nauthor={Fan, Jingjing and Qin, Xiaolong and Tan, Bing},\ntitle={Tseng&#x27;s extragradient algorithm for pseudomonotone variational inequalities on {H}adamard manifolds},\njournal={Applicable Analysis},\nyear={2022},\nvolume={101},\nnumber={6},\npages={2372--2385},\ndoi={10.1080/00036811.2020.1807012},\nurl={https://bingtan.me/files/paper/FQT-AA2022.pdf},\nabstract={In this paper, we investigate the Tseng&#x27;s extragradient algorithm for non-Lipschitzian variational inequalities with pseudomonotone vector fields on Hadamard manifolds. The convergence analysis of the proposed algorithm is discussed under mild assumptions. Two experiments are provided to illustrate the asymptotical behavior of the algorithm. The results presented in this paper generalize some known results presented in the literature.},\nkeywords={Extragradient method,  Hadamard manifolds,  Non-Lipschitz operator,  Pseudomonotone vector field,  Variational inequality problem},\nabbrev_source_title={Appl. Anal.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we investigate the Tseng's extragradient algorithm for non-Lipschitzian variational inequalities with pseudomonotone vector fields on Hadamard manifolds. The convergence analysis of the proposed algorithm is discussed under mild assumptions. Two experiments are provided to illustrate the asymptotical behavior of the algorithm. The results presented in this paper generalize some known results presented in the literature.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-qin-yao-strongconvergenceofselfadaptiveinertialalgorithmsforsolvingsplitvariationalinclusionproblemswithapplications-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Qin, X.;  and Yao, J. C.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Strong convergence of self-adaptive inertial algorithms for solving split variational inclusion problems with applications.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Scientific Computing</i>, 87(1): 20.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><span style=\"color: red\">(ESI Highly Cited Paper)</span></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TQY-JSC2021.pdf\"\n     onclick=\"log_download('tan-qin-yao-strongconvergenceofselfadaptiveinertialalgorithmsforsolvingsplitvariationalinclusionproblemswithapplications-2021', 'https://bingtan.me/files/paper/TQY-JSC2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Strong convergence of self-adaptive inertial algorithms for solving split variational inclusion problems with applications [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s10915-021-01428-9\"\n     onclick=\"log_download('tan-qin-yao-strongconvergenceofselfadaptiveinertialalgorithmsforsolvingsplitvariationalinclusionproblemswithapplications-2021', 'http://doi.org/10.1007/s10915-021-01428-9', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-qin-yao-strongconvergenceofselfadaptiveinertialalgorithmsforsolvingsplitvariationalinclusionproblemswithapplications-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-qin-yao-strongconvergenceofselfadaptiveinertialalgorithmsforsolvingsplitvariationalinclusionproblemswithapplications-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TQY_JSC21,\nauthor={Tan, Bing and Qin, Xiaolong and Yao, Jen C.},\ntitle={Strong convergence of self-adaptive inertial algorithms for solving split variational inclusion problems with applications},\njournal={Journal of Scientific Computing},\nyear={2021},\nvolume={87},\nnumber={1},\ndoi={10.1007/s10915-021-01428-9},\npages={20},\nurl={https://bingtan.me/files/paper/TQY-JSC2021.pdf},\nabstract={In this paper, four self-adaptive iterative algorithms with inertial effects are introduced to solve a split variational inclusion problem in real Hilbert spaces. One of the advantages of the suggested algorithms is that they can work without knowing the prior information of the operator norm. Strong convergence theorems of these algorithms are established under mild and standard assumptions. As applications, the split feasibility problem and the split minimization problem in real Hilbert spaces are studied. Finally, several preliminary numerical experiments as well as an example in the field of compressed sensing are proposed to support the advantages and efficiency of the suggested methods over some existing ones.},\nkeywords={Inertial method,  Mann method,  Signal processing problem,  Split variational inclusion problem,  Strong convergence,  Viscosity method},\nabbrev_source_title={J. Sci. Comput.},\nbibbase_note={&lt;span style=&quot;color: red&quot;&gt;(ESI Highly Cited Paper)&lt;/span&gt;},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, four self-adaptive iterative algorithms with inertial effects are introduced to solve a split variational inclusion problem in real Hilbert spaces. One of the advantages of the suggested algorithms is that they can work without knowing the prior information of the operator norm. Strong convergence theorems of these algorithms are established under mild and standard assumptions. As applications, the split feasibility problem and the split minimization problem in real Hilbert spaces are studied. Finally, several preliminary numerical experiments as well as an example in the field of compressed sensing are proposed to support the advantages and efficiency of the suggested methods over some existing ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-qin-yao-twomodifiedinertialprojectionalgorithmsforbilevelpseudomonotonevariationalinequalitieswithapplicationstooptimalcontrolproblems-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Qin, X.;  and Yao, J. C.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Two modified inertial projection algorithms for bilevel pseudomonotone variational inequalities with applications to optimal control problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Numerical Algorithms</i>, 88(4): 1757–1786.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TQY-NUMA2021.pdf\"\n     onclick=\"log_download('tan-qin-yao-twomodifiedinertialprojectionalgorithmsforbilevelpseudomonotonevariationalinequalitieswithapplicationstooptimalcontrolproblems-2021', 'https://bingtan.me/files/paper/TQY-NUMA2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Two modified inertial projection algorithms for bilevel pseudomonotone variational inequalities with applications to optimal control problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s11075-021-01093-x\"\n     onclick=\"log_download('tan-qin-yao-twomodifiedinertialprojectionalgorithmsforbilevelpseudomonotonevariationalinequalitieswithapplicationstooptimalcontrolproblems-2021', 'http://doi.org/10.1007/s11075-021-01093-x', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-qin-yao-twomodifiedinertialprojectionalgorithmsforbilevelpseudomonotonevariationalinequalitieswithapplicationstooptimalcontrolproblems-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-qin-yao-twomodifiedinertialprojectionalgorithmsforbilevelpseudomonotonevariationalinequalitieswithapplicationstooptimalcontrolproblems-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TQY_NUMA21,\nauthor={Tan, Bing and Qin, Xiaolong and Yao, Jen C.},\ntitle={Two modified inertial projection algorithms for bilevel pseudomonotone variational inequalities with applications to optimal control problems},\njournal={Numerical Algorithms},\nyear={2021},\nvolume={88},\nnumber={4},\npages={1757--1786},\ndoi={10.1007/s11075-021-01093-x},\nurl={https://bingtan.me/files/paper/TQY-NUMA2021.pdf},\nabstract={In this paper, we investigate two new algorithms for solving bilevel pseudomonotone variational inequality problems in real Hilbert spaces. The advantages of our algorithms are that they only need to calculate one projection on the feasible set in each iteration, and do not require the prior information of the Lipschitz constant of the cost operator. Furthermore, two new algorithms are derived to solve variational inequality problems. We establish the strong convergence of the proposed algorithms under some suitable conditions imposed on parameters. Finally, several numerical results and applications in optimal control problems are reported to illustrate the efficiency and advantages of the proposed algorithms.},\nkeywords={Bilevel variational inequality problem,  Hybrid steepest descent method,  Inertial extragradient method,  Projection and contraction method,  Pseudomonotone operator},\nabbrev_source_title={Numer. Algorithms},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we investigate two new algorithms for solving bilevel pseudomonotone variational inequality problems in real Hilbert spaces. The advantages of our algorithms are that they only need to calculate one projection on the feasible set in each iteration, and do not require the prior information of the Lipschitz constant of the cost operator. Furthermore, two new algorithms are derived to solve variational inequality problems. We establish the strong convergence of the proposed algorithms under some suitable conditions imposed on parameters. Finally, several numerical results and applications in optimal control problems are reported to illustrate the efficiency and advantages of the proposed algorithms.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-liu-qin-selfadaptiveinertialextragradientalgorithmsforsolvingbilevelpseudomonotonevariationalinequalityproblems-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Liu, L.;  and Qin, X.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Self adaptive inertial extragradient algorithms for solving bilevel pseudomonotone variational inequality problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Japan Journal of Industrial and Applied Mathematics</i>, 38(2): 519-543.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><span style=\"color: red\">(<s>ESI Highly Cited Paper</s>)</span></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TLQ-JIAM2021.pdf\"\n     onclick=\"log_download('tan-liu-qin-selfadaptiveinertialextragradientalgorithmsforsolvingbilevelpseudomonotonevariationalinequalityproblems-2021', 'https://bingtan.me/files/paper/TLQ-JIAM2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Self adaptive inertial extragradient algorithms for solving bilevel pseudomonotone variational inequality problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s13160-020-00450-y\"\n     onclick=\"log_download('tan-liu-qin-selfadaptiveinertialextragradientalgorithmsforsolvingbilevelpseudomonotonevariationalinequalityproblems-2021', 'http://doi.org/10.1007/s13160-020-00450-y', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-liu-qin-selfadaptiveinertialextragradientalgorithmsforsolvingbilevelpseudomonotonevariationalinequalityproblems-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-liu-qin-selfadaptiveinertialextragradientalgorithmsforsolvingbilevelpseudomonotonevariationalinequalityproblems-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TLQ_JIAM21,\nauthor={Tan, Bing and Liu, Liya and Qin, Xiaolong},\ntitle={Self adaptive inertial extragradient algorithms for solving bilevel pseudomonotone variational inequality problems},\njournal={Japan Journal of Industrial and Applied Mathematics},\nyear={2021},\nvolume={38},\nnumber={2},\npages={519-543},\ndoi={10.1007/s13160-020-00450-y},\nurl={https://bingtan.me/files/paper/TLQ-JIAM2021.pdf},\nabstract={We introduce two inertial extragradient algorithms for solving a bilevel pseudomonotone variational inequality problem in real Hilbert spaces. The advantages of the proposed algorithms are that they can work without the prior knowledge of the Lipschitz constant of the involving operator and only one projection onto the feasible set is required. Strong convergence theorems of the suggested algorithms are obtained under suitable conditions. Finally, some numerical examples are provided to show the efficiency of the proposed algorithms.},\nkeywords={Bilevel variational inequality problem,  Inertial method, Subgradient extragradient method,  Tseng&#x27;s extragradient method,  Pseudomonotone operator,  Hybrid steepest descent method},\nabbrev_source_title={Jpn J. Ind. Appl. Math.},\nbibbase_note={&lt;span style=&quot;color: red&quot;&gt;(&lt;s&gt;ESI Highly Cited Paper&lt;/s&gt;)&lt;/span&gt;},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We introduce two inertial extragradient algorithms for solving a bilevel pseudomonotone variational inequality problem in real Hilbert spaces. The advantages of the proposed algorithms are that they can work without the prior knowledge of the Lipschitz constant of the involving operator and only one projection onto the feasible set is required. Strong convergence theorems of the suggested algorithms are obtained under suitable conditions. Finally, some numerical examples are provided to show the efficiency of the proposed algorithms.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-fan-qin-inertialextragradientalgorithmswithnonmonotonicstepsizesforsolvingvariationalinequalitiesandfixedpointproblems-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Fan, J.;  and Qin, X.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Inertial extragradient algorithms with non-monotonic step sizes for solving variational inequalities and fixed point problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Advances in Operator Theory</i>, 6(4): 61.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TFQ-AIOT2021.pdf\"\n     onclick=\"log_download('tan-fan-qin-inertialextragradientalgorithmswithnonmonotonicstepsizesforsolvingvariationalinequalitiesandfixedpointproblems-2021', 'https://bingtan.me/files/paper/TFQ-AIOT2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Inertial extragradient algorithms with non-monotonic step sizes for solving variational inequalities and fixed point problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s43036-021-00155-0\"\n     onclick=\"log_download('tan-fan-qin-inertialextragradientalgorithmswithnonmonotonicstepsizesforsolvingvariationalinequalitiesandfixedpointproblems-2021', 'http://doi.org/10.1007/s43036-021-00155-0', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-fan-qin-inertialextragradientalgorithmswithnonmonotonicstepsizesforsolvingvariationalinequalitiesandfixedpointproblems-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-fan-qin-inertialextragradientalgorithmswithnonmonotonicstepsizesforsolvingvariationalinequalitiesandfixedpointproblems-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TFQ_AIOT21,\nauthor={Tan, Bing and Fan, Jingjing and Qin, Xiaolong},\ntitle={Inertial extragradient algorithms with non-monotonic step sizes for solving variational inequalities and fixed point problems},\njournal={Advances in Operator Theory},\nyear={2021},\nvolume={6},\nnumber={4},\ndoi={10.1007/s43036-021-00155-0},\npages={61},\nurl={https://bingtan.me/files/paper/TFQ-AIOT2021.pdf},\nabstract={In this paper, we introduce four inertial extragradient algorithms with non-monotonic step sizes to find the solution of the convex feasibility problem, which consists of a monotone variational inequality problem and a fixed point problem with a demicontractive mapping. Strong convergence theorems of the suggested algorithms are established under some standard conditions. Finally, we implement some computational tests to show the efficiency and advantages of the proposed algorithms and compare them with some existing ones.},\nkeywords={Fixed point problem,  Inertial method,  Strong convergence,  Subgradient extragradient method,  Tseng&#x27;s extragradient method,  Variational inequality problem},\nabbrev_source_title={Adv. Oper. Theory},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we introduce four inertial extragradient algorithms with non-monotonic step sizes to find the solution of the convex feasibility problem, which consists of a monotone variational inequality problem and a fixed point problem with a demicontractive mapping. Strong convergence theorems of the suggested algorithms are established under some standard conditions. Finally, we implement some computational tests to show the efficiency and advantages of the proposed algorithms and compare them with some existing ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-li-qin-selfadaptiveinertialsingleprojectionmethodsforvariationalinequalitiesinvolvingnonlipschitzandlipschitzoperatorswiththeirapplicationstooptimalcontrolproblems-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Li, S.;  and Qin, X.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Self-adaptive inertial single projection methods for variational inequalities involving non-Lipschitz and Lipschitz operators with their applications to optimal control problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Applied Numerical Mathematics</i>, 170: 219–241.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TLQ-ANM2021.pdf\"\n     onclick=\"log_download('tan-li-qin-selfadaptiveinertialsingleprojectionmethodsforvariationalinequalitiesinvolvingnonlipschitzandlipschitzoperatorswiththeirapplicationstooptimalcontrolproblems-2021', 'https://bingtan.me/files/paper/TLQ-ANM2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Self-adaptive inertial single projection methods for variational inequalities involving non-Lipschitz and Lipschitz operators with their applications to optimal control problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1016/j.apnum.2021.07.022\"\n     onclick=\"log_download('tan-li-qin-selfadaptiveinertialsingleprojectionmethodsforvariationalinequalitiesinvolvingnonlipschitzandlipschitzoperatorswiththeirapplicationstooptimalcontrolproblems-2021', 'http://doi.org/10.1016/j.apnum.2021.07.022', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-li-qin-selfadaptiveinertialsingleprojectionmethodsforvariationalinequalitiesinvolvingnonlipschitzandlipschitzoperatorswiththeirapplicationstooptimalcontrolproblems-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-li-qin-selfadaptiveinertialsingleprojectionmethodsforvariationalinequalitiesinvolvingnonlipschitzandlipschitzoperatorswiththeirapplicationstooptimalcontrolproblems-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TLQ_ANM21,\nauthor={Tan, Bing and Li, Songxiao and Qin, Xiaolong},\ntitle={Self-adaptive inertial single projection methods for variational inequalities involving non-Lipschitz and Lipschitz operators with their applications to optimal control problems},\njournal={Applied Numerical Mathematics},\nyear={2021},\nvolume={170},\npages={219--241},\ndoi={10.1016/j.apnum.2021.07.022},\nurl={https://bingtan.me/files/paper/TLQ-ANM2021.pdf},\nabstract={In this paper, four accelerated subgradient extragradient methods are proposed to solve the variational inequality problem with a pseudo-monotone operator in real Hilbert spaces. These iterative schemes employ two new adaptive stepsize strategies that are significant when the Lipschitz constant of the mapping involved is unknown. Strong convergence theorems for the proposed algorithms are established under the condition that the operators are Lipschitz continuous and non-Lipschitz continuous. Numerical experiments on finite- and infinite-dimensional spaces and applications in optimal control problems are reported to demonstrate the advantages and efficiency of the proposed algorithms over some existing results.},\nkeywords={Inertial method, Subgradient extragradient method,  Optimal control problem,  Pseudomonotone operator,  Non-Lipschitz operator,  Variational inequality problem},\nabbrev_source_title={Appl Numer Math},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, four accelerated subgradient extragradient methods are proposed to solve the variational inequality problem with a pseudo-monotone operator in real Hilbert spaces. These iterative schemes employ two new adaptive stepsize strategies that are significant when the Lipschitz constant of the mapping involved is unknown. Strong convergence theorems for the proposed algorithms are established under the condition that the operators are Lipschitz continuous and non-Lipschitz continuous. Numerical experiments on finite- and infinite-dimensional spaces and applications in optimal control problems are reported to demonstrate the advantages and efficiency of the proposed algorithms over some existing results.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-li-qin-anacceleratedextragradientalgorithmforbilevelpseudomonotonevariationalinequalityproblemswithapplicationtooptimalcontrolproblems-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Li, S.;  and Qin, X.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  An accelerated extragradient algorithm for bilevel pseudomonotone variational inequality problems with application to optimal control problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas</i>, 115(4): 174.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TLQ-RACSAM2021.pdf\"\n     onclick=\"log_download('tan-li-qin-anacceleratedextragradientalgorithmforbilevelpseudomonotonevariationalinequalityproblemswithapplicationtooptimalcontrolproblems-2021', 'https://bingtan.me/files/paper/TLQ-RACSAM2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"An accelerated extragradient algorithm for bilevel pseudomonotone variational inequality problems with application to optimal control problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s13398-021-01116-1\"\n     onclick=\"log_download('tan-li-qin-anacceleratedextragradientalgorithmforbilevelpseudomonotonevariationalinequalityproblemswithapplicationtooptimalcontrolproblems-2021', 'http://doi.org/10.1007/s13398-021-01116-1', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-li-qin-anacceleratedextragradientalgorithmforbilevelpseudomonotonevariationalinequalityproblemswithapplicationtooptimalcontrolproblems-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-li-qin-anacceleratedextragradientalgorithmforbilevelpseudomonotonevariationalinequalityproblemswithapplicationtooptimalcontrolproblems-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TLQ_RCSM21,\nauthor={Tan, Bing and Li, Songxiao and Qin, Xiaolong},\ntitle={An accelerated extragradient algorithm for bilevel pseudomonotone variational inequality problems with application to optimal control problems},\njournal={Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas},\nyear={2021},\nvolume={115},\nnumber={4},\ndoi={10.1007/s13398-021-01116-1},\npages={174},\nurl={https://bingtan.me/files/paper/TLQ-RACSAM2021.pdf},\nabstract={In this paper, an inertial extragradient algorithm with a new non-monotonic stepsize is proposed to solve the bilevel pseudomonotone variational inequality problem in real Hilbert spaces. The advantages of the suggested iterative algorithm are that only one projection onto the feasible set needs to be performed in each iteration and the prior knowledge of the Lipschitz constant of the mapping involved does not require to be known. The strong convergence theorem of the suggested algorithm is established under some suitable conditions. Numerical experiments are reported to illustrate the advantages and efficiency of the presented algorithm over the existing related ones.},\nkeywords={Bilevel variational inequality problem,  Hybrid steepest descent method,  Inertial extragradient method,  Projection and contraction method,  Pseudomonotone operator},\nabbrev_source_title={Rev. R. Acad. Cienc. Exactas F{\\&#x27; i}s. Nat. Ser. A Mat. RACSAM},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, an inertial extragradient algorithm with a new non-monotonic stepsize is proposed to solve the bilevel pseudomonotone variational inequality problem in real Hilbert spaces. The advantages of the suggested iterative algorithm are that only one projection onto the feasible set needs to be performed in each iteration and the prior knowledge of the Lipschitz constant of the mapping involved does not require to be known. The strong convergence theorem of the suggested algorithm is established under some suitable conditions. Numerical experiments are reported to illustrate the advantages and efficiency of the presented algorithm over the existing related ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-li-qin-onmodifiedsubgradientextragradientmethodsforpseudomonotonevariationalinequalityproblemswithapplications-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Li, S.;  and Qin, X.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  On modified subgradient extragradient methods for pseudomonotone variational inequality problems with applications.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Computational and Applied Mathematics</i>, 40(7): 253.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TLQ-COAM2021.pdf\"\n     onclick=\"log_download('tan-li-qin-onmodifiedsubgradientextragradientmethodsforpseudomonotonevariationalinequalityproblemswithapplications-2021', 'https://bingtan.me/files/paper/TLQ-COAM2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"On modified subgradient extragradient methods for pseudomonotone variational inequality problems with applications [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s40314-021-01642-z\"\n     onclick=\"log_download('tan-li-qin-onmodifiedsubgradientextragradientmethodsforpseudomonotonevariationalinequalityproblemswithapplications-2021', 'http://doi.org/10.1007/s40314-021-01642-z', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-li-qin-onmodifiedsubgradientextragradientmethodsforpseudomonotonevariationalinequalityproblemswithapplications-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-li-qin-onmodifiedsubgradientextragradientmethodsforpseudomonotonevariationalinequalityproblemswithapplications-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TLQ_COAM21,\nauthor={Tan, Bing and Li, Songxiao and Qin, Xiaolong},\ntitle={On modified subgradient extragradient methods for pseudomonotone variational inequality problems with applications},\njournal={Computational and Applied Mathematics},\nyear={2021},\nvolume={40},\nnumber={7},\ndoi={10.1007/s40314-021-01642-z},\npages={253},\nurl={https://bingtan.me/files/paper/TLQ-COAM2021.pdf},\nabstract={This paper presents several modified subgradient extragradient methods with inertial effects to approximate solutions of variational inequality problems in real Hilbert spaces. The operators involved are either pseudomonotone Lipschitz continuous or pseudomonotone non-Lipschitz continuous. The advantage of the suggested algorithms is that they can work adaptively without the prior information of the Lipschitz constant of the mapping involved. Strong convergence theorems of the proposed algorithms are established under some suitable conditions. Finally, some numerical experiments are given to verify the advantages and efficiency of the proposed iterative algorithms with respect to previously known ones.},\nkeywords={Extragradient method,  Non-Lipschitz operator,  Optimal control problem,  Pseudomonotone operator,  Variational inequality problem},\nabbrev_source_title={Comput. Appl. Math.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This paper presents several modified subgradient extragradient methods with inertial effects to approximate solutions of variational inequality problems in real Hilbert spaces. The operators involved are either pseudomonotone Lipschitz continuous or pseudomonotone non-Lipschitz continuous. The advantage of the suggested algorithms is that they can work adaptively without the prior information of the Lipschitz constant of the mapping involved. Strong convergence theorems of the proposed algorithms are established under some suitable conditions. Finally, some numerical experiments are given to verify the advantages and efficiency of the proposed iterative algorithms with respect to previously known ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-fan-li-selfadaptiveinertialextragradientalgorithmsforsolvingvariationalinequalityproblems-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Fan, J.;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Self-adaptive inertial extragradient algorithms for solving variational inequality problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Computational and Applied Mathematics</i>, 40(1): 19.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><span style=\"color: red\">(<s>ESI Highly Cited Paper</s>)</span></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TFL-COAM2021.pdf\"\n     onclick=\"log_download('tan-fan-li-selfadaptiveinertialextragradientalgorithmsforsolvingvariationalinequalityproblems-2021', 'https://bingtan.me/files/paper/TFL-COAM2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Self-adaptive inertial extragradient algorithms for solving variational inequality problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s40314-020-01393-3\"\n     onclick=\"log_download('tan-fan-li-selfadaptiveinertialextragradientalgorithmsforsolvingvariationalinequalityproblems-2021', 'http://doi.org/10.1007/s40314-020-01393-3', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-fan-li-selfadaptiveinertialextragradientalgorithmsforsolvingvariationalinequalityproblems-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-fan-li-selfadaptiveinertialextragradientalgorithmsforsolvingvariationalinequalityproblems-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TFL_COAM21,\nauthor={Tan, Bing and Fan, Jingjing and Li, Songxiao},\ntitle={Self-adaptive inertial extragradient algorithms for solving variational inequality problems},\njournal={Computational and Applied Mathematics},\nyear={2021},\nvolume={40},\nnumber={1},\ndoi={10.1007/s40314-020-01393-3},\npages={19},\nurl={https://bingtan.me/files/paper/TFL-COAM2021.pdf},\nabstract={In this paper, we study the strong convergence of two Mann-type inertial extragradient algorithms, which are devised with a new step size, for solving a variational inequality problem with a monotone and Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems for the suggested algorithms are proved without the prior knowledge of the Lipschitz constant of the operator. Finally, we provide some numerical experiments to illustrate the performance of the proposed algorithms and provide a comparison with related ones.},\nkeywords={Inertial method,  Mann method,  Subgradient extragradient method,  Tseng&#x27;s extragradient method,  Variational inequality problem},\nabbrev_source_title={Comput. Appl. Math.},\nbibbase_note={&lt;span style=&quot;color: red&quot;&gt;(&lt;s&gt;ESI Highly Cited Paper&lt;/s&gt;)&lt;/span&gt;},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we study the strong convergence of two Mann-type inertial extragradient algorithms, which are devised with a new step size, for solving a variational inequality problem with a monotone and Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems for the suggested algorithms are proved without the prior knowledge of the Lipschitz constant of the operator. Finally, we provide some numerical experiments to illustrate the performance of the proposed algorithms and provide a comparison with related ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-cho-selfadaptiveinertialshrinkingprojectionalgorithmsforsolvingpseudomonotonevariationalinequalities-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Cho, S. Y.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Self-adaptive inertial shrinking projection algorithms for solving pseudomonotone variational inequalities.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Nonlinear and Convex Analysis</i>, 22(3): 613–627.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TC-JNCA2021.pdf\"\n     onclick=\"log_download('tan-cho-selfadaptiveinertialshrinkingprojectionalgorithmsforsolvingpseudomonotonevariationalinequalities-2021', 'https://bingtan.me/files/paper/TC-JNCA2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Self-adaptive inertial shrinking projection algorithms for solving pseudomonotone variational inequalities [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-cho-selfadaptiveinertialshrinkingprojectionalgorithmsforsolvingpseudomonotonevariationalinequalities-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-cho-selfadaptiveinertialshrinkingprojectionalgorithmsforsolvingpseudomonotonevariationalinequalities-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TC_JNCA21,\nauthor={Tan, Bing and Cho, Sun Y.},\ntitle={Self-adaptive inertial shrinking projection algorithms for solving pseudomonotone variational inequalities},\njournal={Journal of Nonlinear and Convex Analysis},\nyear={2021},\nvolume={22},\nnumber={3},\npages={613--627},\nurl={https://bingtan.me/files/paper/TC-JNCA2021.pdf},\nabstract={In this paper, we construct two fast iterative methods to solve pseudomonotone variational inequalities in real Hilbert spaces. The advantage of the suggested iterative schemes is that they can adaptively update the iterative step size through some previously known information without performing any line search process. Strong convergence theorems of the proposed algorithms are established under some relaxed conditions imposed on the parameters. Finally, several numerical tests are given to show the advantages and efficiency of the proposed approaches compared with the existing results.},\nkeywords={Inertial method, Subgradient extragradient method,  Tseng&#x27;s extragradient method,  Pseudomonotone operator,  Shrinking projection method,  Variational inequality problem},\nabbrev_source_title={J. Nonlinear Convex Anal.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we construct two fast iterative methods to solve pseudomonotone variational inequalities in real Hilbert spaces. The advantage of the suggested iterative schemes is that they can adaptively update the iterative step size through some previously known information without performing any line search process. Strong convergence theorems of the proposed algorithms are established under some relaxed conditions imposed on the parameters. Finally, several numerical tests are given to show the advantages and efficiency of the proposed approaches compared with the existing results.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-cho-inertialextragradientmethodsforsolvingpseudomonotonevariationalinequalitieswithnonlipschitzmappingsandtheiroptimizationapplications-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Cho, S. Y.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Inertial extragradient methods for solving pseudomonotone variational inequalities with non-lipschitz mappings and their optimization applications.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Applied Set-Valued Analysis and Optimization</i>, 3(2): 165–192.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TC-ASVAO2021.pdf\"\n     onclick=\"log_download('tan-cho-inertialextragradientmethodsforsolvingpseudomonotonevariationalinequalitieswithnonlipschitzmappingsandtheiroptimizationapplications-2021', 'https://bingtan.me/files/paper/TC-ASVAO2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Inertial extragradient methods for solving pseudomonotone variational inequalities with non-lipschitz mappings and their optimization applications [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.23952/asvao.3.2021.2.03\"\n     onclick=\"log_download('tan-cho-inertialextragradientmethodsforsolvingpseudomonotonevariationalinequalitieswithnonlipschitzmappingsandtheiroptimizationapplications-2021', 'http://doi.org/10.23952/asvao.3.2021.2.03', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-cho-inertialextragradientmethodsforsolvingpseudomonotonevariationalinequalitieswithnonlipschitzmappingsandtheiroptimizationapplications-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-cho-inertialextragradientmethodsforsolvingpseudomonotonevariationalinequalitieswithnonlipschitzmappingsandtheiroptimizationapplications-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TC_ASVAO21,\nauthor={Tan, Bing and Cho, Sun Y.},\ntitle={Inertial extragradient methods for solving pseudomonotone variational inequalities with non-lipschitz mappings and their optimization applications},\njournal={Applied Set-Valued Analysis and Optimization},\nyear={2021},\nvolume={3},\nnumber={2},\npages={165--192},\ndoi={10.23952/asvao.3.2021.2.03},\nurl={https://bingtan.me/files/paper/TC-ASVAO2021.pdf},\nabstract={In this paper, four extragradient-type algorithms with inertial terms are presented for solving the variational inequality problem with a pseudomonotone and non-Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems of the suggested methods are established under some suitable conditions imposed on the parameters. Finally, several computational tests and applications in optimal control problems are given to illustrate the efficiency and advantages of the proposed iterative schemes over some known ones.},\nkeywords={Inertial extragradient method,  Non-Lipschitz operator,  Pseudomonotone operator,  Variational inequality problem,  Viscosity method},\nabbrev_source_title={Appl. Set-Valued. Anal. Optim.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, four extragradient-type algorithms with inertial terms are presented for solving the variational inequality problem with a pseudomonotone and non-Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems of the suggested methods are established under some suitable conditions imposed on the parameters. Finally, several computational tests and applications in optimal control problems are given to illustrate the efficiency and advantages of the proposed iterative schemes over some known ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"liu-tan-latif-approximationoffixedpointsforasemigroupofbregmanquasinonexpansivemappingsinbanachspaces-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Liu, L.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Latif, A.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Approximation of fixed points for a semigroup of Bregman quasi-nonexpansive mappings in Banach spaces.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Nonlinear and Variational Analysis</i>, 5(1): 9–22.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/LTL-JNVA2021.pdf\"\n     onclick=\"log_download('liu-tan-latif-approximationoffixedpointsforasemigroupofbregmanquasinonexpansivemappingsinbanachspaces-2021', 'https://bingtan.me/files/paper/LTL-JNVA2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Approximation of fixed points for a semigroup of Bregman quasi-nonexpansive mappings in Banach spaces [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.23952/jnva.5.2021.1.02\"\n     onclick=\"log_download('liu-tan-latif-approximationoffixedpointsforasemigroupofbregmanquasinonexpansivemappingsinbanachspaces-2021', 'http://doi.org/10.23952/jnva.5.2021.1.02', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/liu-tan-latif-approximationoffixedpointsforasemigroupofbregmanquasinonexpansivemappingsinbanachspaces-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('liu-tan-latif-approximationoffixedpointsforasemigroupofbregmanquasinonexpansivemappingsinbanachspaces-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{LTL_JNVA21,\nauthor={Liu, Liya and Tan, Bing and Latif, A.},\ntitle={Approximation of fixed points for a semigroup of Bregman quasi-nonexpansive mappings in {B}anach spaces},\njournal={Journal of Nonlinear and Variational Analysis},\nyear={2021},\nvolume={5},\nnumber={1},\npages={9--22},\ndoi={10.23952/jnva.5.2021.1.02},\nurl={https://bingtan.me/files/paper/LTL-JNVA2021.pdf},\nabstract={The purpose of this paper is to study the iterative scheme of the Halpern type for a commutative semigroup $\\mathfrak{J}=\\left\\{S_{\\lambda}: \\lambda \\in \\mathcal{Q}\\right\\}$ of Bregman quasi-nonexpansive mappings on a closed and convex subset of a Banach space. A strong convergence theorem is established for finding a common fixed point solution. Our results extend and improve some related results in the current literature. In addition, we present numerical examples to illustrate the performance of our method in finite and infinite dimensional spaces.},\nkeywords={Banach space,  Bregman quasi-nonexpansive,  Fixed point problem,  Halpern method,  Strong convergence},\nabbrev_source_title={J. Nonlinear Var. Anal.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  The purpose of this paper is to study the iterative scheme of the Halpern type for a commutative semigroup $\\mathfrak{J}=łeft\\{S_{λ}: λ ∈ \\mathcal{Q}i̊ght\\}$ of Bregman quasi-nonexpansive mappings on a closed and convex subset of a Banach space. A strong convergence theorem is established for finding a common fixed point solution. Our results extend and improve some related results in the current literature. In addition, we present numerical examples to illustrate the performance of our method in finite and infinite dimensional spaces.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"zhou-tan-li-anacceleratedhybridprojectionmethodwithaselfadaptivestepsizesequenceforsolvingsplitcommonfixedpointproblems-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Zhou, Z.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  An accelerated hybrid projection method with a self-adaptive step-size sequence for solving split common fixed point problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Mathematical Methods in the Applied Sciences</i>, 44(8): 7294–7303.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><span style=\"color: red\">(<s>ESI Highly Cited Paper</s>)</span></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/ZTL-MMAS2021.pdf\"\n     onclick=\"log_download('zhou-tan-li-anacceleratedhybridprojectionmethodwithaselfadaptivestepsizesequenceforsolvingsplitcommonfixedpointproblems-2021', 'https://bingtan.me/files/paper/ZTL-MMAS2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"An accelerated hybrid projection method with a self-adaptive step-size sequence for solving split common fixed point problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1002/mma.7261\"\n     onclick=\"log_download('zhou-tan-li-anacceleratedhybridprojectionmethodwithaselfadaptivestepsizesequenceforsolvingsplitcommonfixedpointproblems-2021', 'http://doi.org/10.1002/mma.7261', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/zhou-tan-li-anacceleratedhybridprojectionmethodwithaselfadaptivestepsizesequenceforsolvingsplitcommonfixedpointproblems-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('zhou-tan-li-anacceleratedhybridprojectionmethodwithaselfadaptivestepsizesequenceforsolvingsplitcommonfixedpointproblems-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{ZTL_MMAS21,\nauthor={Zhou, Zheng and Tan, Bing and Li, Songxiao},\ntitle={An accelerated hybrid projection method with a self-adaptive step-size sequence for solving split common fixed point problems},\njournal={Mathematical Methods in the Applied Sciences},\nyear={2021},\nvolume={44},\nnumber={8},\npages={7294--7303},\ndoi={10.1002/mma.7261},\nurl={https://bingtan.me/files/paper/ZTL-MMAS2021.pdf},\nabstract={This paper attempts to solve the split common fixed point problem for demicontractive mappings. We give an accelerated hybrid projection algorithm that combines the hybrid projection method and the inertial technique. The strong convergence theorem of this algorithm is obtained under mild conditions by a self-adaptive step-size sequence, which does not need prior knowledge of the operator norm. Some numerical experiments in infinite-dimensional Hilbert spaces are provided to illustrate the reliability and robustness of the algorithm and also to compare it with existing ones.},\nkeywords={Demicontractive mapping,  Hybrid projection method,  Inertial method,  Split common fixed point problem},\nabbrev_source_title={Math. Methods Appl. Sci.},\nbibbase_note={&lt;span style=&quot;color: red&quot;&gt;(&lt;s&gt;ESI Highly Cited Paper&lt;/s&gt;)&lt;/span&gt;},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This paper attempts to solve the split common fixed point problem for demicontractive mappings. We give an accelerated hybrid projection algorithm that combines the hybrid projection method and the inertial technique. The strong convergence theorem of this algorithm is obtained under mild conditions by a self-adaptive step-size sequence, which does not need prior knowledge of the operator norm. Some numerical experiments in infinite-dimensional Hilbert spaces are provided to illustrate the reliability and robustness of the algorithm and also to compare it with existing ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"fan-tan-li-anexplicitextragradientalgorithmforequilibriumproblemsonhhadamardmanifolds-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Fan, J.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  An explicit extragradient algorithm for equilibrium problems on HHadamard manifolds.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Computational and Applied Mathematics</i>, 40(2): 68.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/FTL-COAM2021.pdf\"\n     onclick=\"log_download('fan-tan-li-anexplicitextragradientalgorithmforequilibriumproblemsonhhadamardmanifolds-2021', 'https://bingtan.me/files/paper/FTL-COAM2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"An explicit extragradient algorithm for equilibrium problems on HHadamard manifolds [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s40314-021-01427-4\"\n     onclick=\"log_download('fan-tan-li-anexplicitextragradientalgorithmforequilibriumproblemsonhhadamardmanifolds-2021', 'http://doi.org/10.1007/s40314-021-01427-4', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/fan-tan-li-anexplicitextragradientalgorithmforequilibriumproblemsonhhadamardmanifolds-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('fan-tan-li-anexplicitextragradientalgorithmforequilibriumproblemsonhhadamardmanifolds-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{FTL_COAM21,\nauthor={Fan, Jingjing and Tan, Bing and Li, Songxiao},\ntitle={An explicit extragradient algorithm for equilibrium problems on {H}{H}adamard manifolds},\njournal={Computational and Applied Mathematics},\nyear={2021},\nvolume={40},\nnumber={2},\ndoi={10.1007/s40314-021-01427-4},\npages={68},\nurl={https://bingtan.me/files/paper/FTL-COAM2021.pdf},\nabstract={In this paper, we investigate a new extragradient algorithm for solving pseudomonotone equilibrium problems on Hadamard manifolds. Our algorithm uses a variable stepsize, which is updated at each iteration and based on some previous iterates. The convergence analysis of the proposed algorithm is discussed under mild assumptions. In the case where the equilibrium bifunction is strongly pseudomonotone, the R-linear rate of convergence of the new algorithm is formulated. A fundamental experiment is provided to illustrate the numerical behavior of the algorithm.},\nkeywords={Equilibrium problem,  Extragradient method,  Hadamard manifolds,  Lipschitz-type bifunction,  Pseudomonotone bifunction},\nabbrev_source_title={Comput. Appl. Math.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we investigate a new extragradient algorithm for solving pseudomonotone equilibrium problems on Hadamard manifolds. Our algorithm uses a variable stepsize, which is updated at each iteration and based on some previous iterates. The convergence analysis of the proposed algorithm is discussed under mild assumptions. In the case where the equilibrium bifunction is strongly pseudomonotone, the R-linear rate of convergence of the new algorithm is formulated. A fundamental experiment is provided to illustrate the numerical behavior of the algorithm.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"fan-qin-tan-convergenceofaninertialshadowdouglasrachfordsplittingalgorithmformonotoneinclusions-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Fan, J.; Qin, X.;  and <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Convergence of an inertial shadow Douglas-Rachford splitting algorithm for monotone inclusions.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Numerical Functional Analysis and Optimization</i>, 42(14): 1627–1644.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/FQT-NFAO2021.pdf\"\n     onclick=\"log_download('fan-qin-tan-convergenceofaninertialshadowdouglasrachfordsplittingalgorithmformonotoneinclusions-2021', 'https://bingtan.me/files/paper/FQT-NFAO2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Convergence of an inertial shadow Douglas-Rachford splitting algorithm for monotone inclusions [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1080/01630563.2021.2001749\"\n     onclick=\"log_download('fan-qin-tan-convergenceofaninertialshadowdouglasrachfordsplittingalgorithmformonotoneinclusions-2021', 'http://doi.org/10.1080/01630563.2021.2001749', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/fan-qin-tan-convergenceofaninertialshadowdouglasrachfordsplittingalgorithmformonotoneinclusions-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('fan-qin-tan-convergenceofaninertialshadowdouglasrachfordsplittingalgorithmformonotoneinclusions-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{FQT_NFAO21,\nauthor={Fan, Jingjing and Qin, Xiaolong and Tan, Bing},\ntitle={Convergence of an inertial shadow {D}ouglas-{R}achford splitting algorithm for monotone inclusions},\njournal={Numerical Functional Analysis and Optimization},\nyear={2021},\nvolume={42},\nnumber={14},\npages={1627--1644},\ndoi={10.1080/01630563.2021.2001749},\nurl={https://bingtan.me/files/paper/FQT-NFAO2021.pdf},\nabstract={An inertial shadow Douglas-Rachford splitting algorithm for finding zeros of the sum of monotone operators is proposed in Hilbert spaces. Moreover, a three-operator splitting algorithm for solving a class of monotone inclusion problems is also concerned. The weak convergence of the algorithms is investigated under mild assumptions. Some numerical experiments are implemented to illustrate our main convergence results.},\nkeywords={Inertial method,  Monotone inclusion,  Shadow Douglas-Rachford splitting algorithm,  Three-operator splitting},\nabbrev_source_title={Numer. Funct. Anal. Optim.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  An inertial shadow Douglas-Rachford splitting algorithm for finding zeros of the sum of monotone operators is proposed in Hilbert spaces. Moreover, a three-operator splitting algorithm for solving a class of monotone inclusion problems is also concerned. The weak convergence of the algorithms is investigated under mild assumptions. Some numerical experiments are implemented to illustrate our main convergence results.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-li-strongconvergenceofinertialmannalgorithmsforsolvinghierarchicalfixedpointproblems-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Strong convergence of inertial mann algorithms for solving hierarchical fixed point problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Nonlinear and Variational Analysis</i>, 4(3): 337–355.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TL-JNVA2020.pdf\"\n     onclick=\"log_download('tan-li-strongconvergenceofinertialmannalgorithmsforsolvinghierarchicalfixedpointproblems-2020', 'https://bingtan.me/files/paper/TL-JNVA2020.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Strong convergence of inertial mann algorithms for solving hierarchical fixed point problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.23952/jnva.4.2020.3.02\"\n     onclick=\"log_download('tan-li-strongconvergenceofinertialmannalgorithmsforsolvinghierarchicalfixedpointproblems-2020', 'http://doi.org/10.23952/jnva.4.2020.3.02', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-li-strongconvergenceofinertialmannalgorithmsforsolvinghierarchicalfixedpointproblems-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-li-strongconvergenceofinertialmannalgorithmsforsolvinghierarchicalfixedpointproblems-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TL_JNVA20,\nauthor={Tan, Bing and Li, Songxiao},\ntitle={Strong convergence of inertial mann algorithms for solving hierarchical fixed point problems},\njournal={Journal of Nonlinear and Variational Analysis},\nyear={2020},\nvolume={4},\nnumber={3},\npages={337--355},\ndoi={10.23952/jnva.4.2020.3.02},\nurl={https://bingtan.me/files/paper/TL-JNVA2020.pdf},\nabstract={The paper introduces two inertial Mann algorithms to find solutions of hierarchical fixed point problems of nonexpansive mappings. We obtain strong convergence theorems in Hilbert spaces under suitable conditions. Some numerical examples are provided to illustrate the numerical behavior of the algorithms and numerical results show that our proposed algorithms are efficient and robust.},\nkeywords={Hierarchical fixed point problem,  Inertial method, Mann method,  Nonexpansive mapping,  Strong convergence,  Viscosity method},\nabbrev_source_title={J. Nonlinear Var. Anal.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  The paper introduces two inertial Mann algorithms to find solutions of hierarchical fixed point problems of nonexpansive mappings. We obtain strong convergence theorems in Hilbert spaces under suitable conditions. Some numerical examples are provided to illustrate the numerical behavior of the algorithms and numerical results show that our proposed algorithms are efficient and robust.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-cho-aninertialmannlikealgorithmforfixedpointsofnonexpansivemappingsinhilbertspaces-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Cho, S. Y.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  An inertial mann-like algorithm for fixed points of nonexpansive mappings in Hilbert spaces.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Applied and Numerical Optimization</i>, 2(3): 335–351.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TC-JANO2020.pdf\"\n     onclick=\"log_download('tan-cho-aninertialmannlikealgorithmforfixedpointsofnonexpansivemappingsinhilbertspaces-2020', 'https://bingtan.me/files/paper/TC-JANO2020.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"An inertial mann-like algorithm for fixed points of nonexpansive mappings in Hilbert spaces [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.23952/jano.2.2020.3.05\"\n     onclick=\"log_download('tan-cho-aninertialmannlikealgorithmforfixedpointsofnonexpansivemappingsinhilbertspaces-2020', 'http://doi.org/10.23952/jano.2.2020.3.05', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-cho-aninertialmannlikealgorithmforfixedpointsofnonexpansivemappingsinhilbertspaces-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>1 download</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-cho-aninertialmannlikealgorithmforfixedpointsofnonexpansivemappingsinhilbertspaces-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TC_JANO20,\nauthor={Tan, Bing and Cho, Sun Y.},\ntitle={An inertial mann-like algorithm for fixed points of nonexpansive mappings in {H}ilbert spaces},\njournal={Journal of Applied and Numerical Optimization},\nyear={2020},\nvolume={2},\nnumber={3},\npages={335--351},\ndoi={10.23952/jano.2.2020.3.05},\nurl={https://bingtan.me/files/paper/TC-JANO2020.pdf},\nabstract={In this paper, we investigate an inertial Mann-like algorithm for fixed points of nonexpansive mappings in Hilbert spaces and obtain strong convergence results under some mild assumptions. Based on this, we derive a forward-backward algorithm involving Tikhonov regularization terms, which converges strongly to the solution of the monotone inclusion problem. We demonstrate the advantages of our algorithms comparing with some existing ones in the literature via split feasibility problem, variational inequality problem and signal recovery problem.},\nkeywords={Forward-backward splitting algorithm,  Inertial method, Mann method,  Nonexpansive mapping,  Strong convergence,  Tikhonov regularization},\nabbrev_source_title={J. Appl. Numer. Optim.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we investigate an inertial Mann-like algorithm for fixed points of nonexpansive mappings in Hilbert spaces and obtain strong convergence results under some mild assumptions. Based on this, we derive a forward-backward algorithm involving Tikhonov regularization terms, which converges strongly to the solution of the monotone inclusion problem. We demonstrate the advantages of our algorithms comparing with some existing ones in the literature via split feasibility problem, variational inequality problem and signal recovery problem.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-xu-strongconvergenceoftwoinertialprojectionalgorithmsinhilbertspaces-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Xu, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Strong convergence of two inertial projection algorithms in Hilbert spaces.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Applied and Numerical Optimization</i>, 2(2): 171–186.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TX-JANO2020.pdf\"\n     onclick=\"log_download('tan-xu-strongconvergenceoftwoinertialprojectionalgorithmsinhilbertspaces-2020', 'https://bingtan.me/files/paper/TX-JANO2020.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Strong convergence of two inertial projection algorithms in Hilbert spaces [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.23952/jano.2.2020.2.04\"\n     onclick=\"log_download('tan-xu-strongconvergenceoftwoinertialprojectionalgorithmsinhilbertspaces-2020', 'http://doi.org/10.23952/jano.2.2020.2.04', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-xu-strongconvergenceoftwoinertialprojectionalgorithmsinhilbertspaces-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-xu-strongconvergenceoftwoinertialprojectionalgorithmsinhilbertspaces-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TX_JANO20,\nauthor={Tan, Bing and Xu, Shanshan},\ntitle={Strong convergence of two inertial projection algorithms in {H}ilbert spaces},\njournal={Journal of Applied and Numerical Optimization},\nyear={2020},\nvolume={2},\nnumber={2},\npages={171--186},\ndoi={10.23952/jano.2.2020.2.04},\nurl={https://bingtan.me/files/paper/TX-JANO2020.pdf},\nabstract={In this paper, we propose two inertial projection algorithms for finding a common solution of monotone variational inclusions and hierarchical fixed point problems of nonexpansive mappings. We obtain two strong convergence theorems under some suitable conditions in Hilbert spaces. In addition, we also give numerical examples to compare our algorithms with the existing ones. Numerical results show that our proposed algorithms are efficient and robust.},\nkeywords={Hierarchical fixed point problem,  Inertial method,  Monotone operator,  Strong convergence,  Inclusion problem},\nabbrev_source_title={J. Appl. Numer. Optim.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we propose two inertial projection algorithms for finding a common solution of monotone variational inclusions and hierarchical fixed point problems of nonexpansive mappings. We obtain two strong convergence theorems under some suitable conditions in Hilbert spaces. In addition, we also give numerical examples to compare our algorithms with the existing ones. Numerical results show that our proposed algorithms are efficient and robust.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-zhou-qin-acceleratedprojectionbasedforwardbackwardsplittingalgorithmsformonotoneinclusionproblems-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Zhou, Z.;  and Qin, X.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Accelerated projection-based forward-backward splitting algorithms for monotone inclusion problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Applied Analysis and Computation</i>, 10(5): 2184–2197.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TZQ-JAAC2020.pdf\"\n     onclick=\"log_download('tan-zhou-qin-acceleratedprojectionbasedforwardbackwardsplittingalgorithmsformonotoneinclusionproblems-2020', 'https://bingtan.me/files/paper/TZQ-JAAC2020.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Accelerated projection-based forward-backward splitting algorithms for monotone inclusion problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.11948/20190363\"\n     onclick=\"log_download('tan-zhou-qin-acceleratedprojectionbasedforwardbackwardsplittingalgorithmsformonotoneinclusionproblems-2020', 'http://doi.org/10.11948/20190363', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-zhou-qin-acceleratedprojectionbasedforwardbackwardsplittingalgorithmsformonotoneinclusionproblems-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-zhou-qin-acceleratedprojectionbasedforwardbackwardsplittingalgorithmsformonotoneinclusionproblems-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TZQ_JAAC20,\nauthor={Tan, Bing and Zhou, Zheng and Qin, Xiaolong},\ntitle={Accelerated projection-based forward-backward splitting algorithms for monotone inclusion problems},\njournal={Journal of Applied Analysis and Computation},\nyear={2020},\nvolume={10},\nnumber={5},\npages={2184--2197},\ndoi={10.11948/20190363},\nurl={https://bingtan.me/files/paper/TZQ-JAAC2020.pdf},\nabstract={In this paper, based on inertial and Tseng&#x27;s ideas, we propose two projection-based algorithms to solve a monotone inclusion problem in infinite dimensional Hilbert spaces. Solution theorems of strong convergence are obtained under the certain conditions. Some numerical experiments are presented to illustrate that our algorithms are efficient than the existing results.},\nkeywords={Forward-backward splitting algorithm,  Inclusion problem,  Monotone operator,  Strong convergence},\nabbrev_source_title={J. Appl. Anal. Comput.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, based on inertial and Tseng's ideas, we propose two projection-based algorithms to solve a monotone inclusion problem in infinite dimensional Hilbert spaces. Solution theorems of strong convergence are obtained under the certain conditions. Some numerical experiments are presented to illustrate that our algorithms are efficient than the existing results.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-xu-li-inertialshrinkingprojectionalgorithmsforsolvinghierarchicalvariationalinequalityproblems-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Xu, S.;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Inertial shrinking projection algorithms for solving hierarchical variational inequality problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Nonlinear and Convex Analysis</i>, 21(4): 871–884.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><span style=\"color: red\">(<s>ESI Highly Cited Paper</s>)</span></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TXL-JNCA2020.pdf\"\n     onclick=\"log_download('tan-xu-li-inertialshrinkingprojectionalgorithmsforsolvinghierarchicalvariationalinequalityproblems-2020', 'https://bingtan.me/files/paper/TXL-JNCA2020.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Inertial shrinking projection algorithms for solving hierarchical variational inequality problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-xu-li-inertialshrinkingprojectionalgorithmsforsolvinghierarchicalvariationalinequalityproblems-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-xu-li-inertialshrinkingprojectionalgorithmsforsolvinghierarchicalvariationalinequalityproblems-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TXL_JNCA20_2,\nauthor={Tan, Bing and Xu, Shanshan and Li, Songxiao},\ntitle={Inertial shrinking projection algorithms for solving hierarchical variational inequality problems},\njournal={Journal of Nonlinear and Convex Analysis},\nyear={2020},\nvolume={21},\nnumber={4},\npages={871--884},\nurl={https://bingtan.me/files/paper/TXL-JNCA2020.pdf},\nabstract={In this paper, we propose two inertial shrinking algorithms to approximate a solution of hierarchical variational inequality problems with nonex-pansive mappings in Hilbert spaces. We prove strong convergence theorems under some mild conditions. Finally, we present some numerical examples to compare our algorithms with some existing algorithms, which illustrate the advantage of our proposed algorithms.},\nkeywords={Hierarchical variational inequality problem,  Inertial method, Mann method,  Nonexpansive mapping,  Shrinking projection method,  Strong convergence},\nabbrev_source_title={J. Nonlinear Convex Anal.},\nbibbase_note={&lt;span style=&quot;color: red&quot;&gt;(&lt;s&gt;ESI Highly Cited Paper&lt;/s&gt;)&lt;/span&gt;},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we propose two inertial shrinking algorithms to approximate a solution of hierarchical variational inequality problems with nonex-pansive mappings in Hilbert spaces. We prove strong convergence theorems under some mild conditions. Finally, we present some numerical examples to compare our algorithms with some existing algorithms, which illustrate the advantage of our proposed algorithms.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-xu-li-inertialhybridandshrinkingprojectionalgorithmsforsolvingvariationalinequalityproblems-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Xu, S.;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Inertial hybrid and shrinking projection algorithms for solving variational inequality problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Nonlinear and Convex Analysis</i>, 21(10): 2193–2206.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TXL-JNCA2020-10.pdf\"\n     onclick=\"log_download('tan-xu-li-inertialhybridandshrinkingprojectionalgorithmsforsolvingvariationalinequalityproblems-2020', 'https://bingtan.me/files/paper/TXL-JNCA2020-10.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Inertial hybrid and shrinking projection algorithms for solving variational inequality problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-xu-li-inertialhybridandshrinkingprojectionalgorithmsforsolvingvariationalinequalityproblems-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-xu-li-inertialhybridandshrinkingprojectionalgorithmsforsolvingvariationalinequalityproblems-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TXL_JNCA20_1,\nauthor={Tan, Bing and Xu, Shanshan and Li, Songxiao},\ntitle={Inertial hybrid and shrinking projection algorithms for solving variational inequality problems},\njournal={Journal of Nonlinear and Convex Analysis},\nyear={2020},\nvolume={21},\nnumber={10},\npages={2193--2206},\nurl={https://bingtan.me/files/paper/TXL-JNCA2020-10.pdf},\nabstract={In this paper, we propose two inertial hybrid and shrinking projection algorithms for strict pseudo-contractions in Hilbert spaces and obtain strong theorems in general conditions. In addition, we also propose two new inertial hybrid and shrinking projection algorithms without extrapolating step for non-expansive mappings in Hilbert spaces and get strong convergence results. Finally, we give some numerical examples to illustrate the computational performance of our proposed algorithms.},\nkeywords={Variational inequality problem,  Inertial method, Hybrid projection method, Shrinking projection method, Strong convergence},\nabbrev_source_title={J. Nonlinear Convex Anal.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we propose two inertial hybrid and shrinking projection algorithms for strict pseudo-contractions in Hilbert spaces and obtain strong theorems in general conditions. In addition, we also propose two new inertial hybrid and shrinking projection algorithms without extrapolating step for non-expansive mappings in Hilbert spaces and get strong convergence results. Finally, we give some numerical examples to illustrate the computational performance of our proposed algorithms.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-xu-li-modifiedinertialhybridandshrinkingprojectionalgorithmsforsolvingfixedpointproblems-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Xu, S.;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Modified inertial hybrid and shrinking projection algorithms for solving fixed point problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Mathematics</i>, 8(2): 236.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TXL-Math2020.pdf\"\n     onclick=\"log_download('tan-xu-li-modifiedinertialhybridandshrinkingprojectionalgorithmsforsolvingfixedpointproblems-2020', 'https://bingtan.me/files/paper/TXL-Math2020.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Modified inertial hybrid and shrinking projection algorithms for solving fixed point problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.3390/math8020236\"\n     onclick=\"log_download('tan-xu-li-modifiedinertialhybridandshrinkingprojectionalgorithmsforsolvingfixedpointproblems-2020', 'http://doi.org/10.3390/math8020236', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-xu-li-modifiedinertialhybridandshrinkingprojectionalgorithmsforsolvingfixedpointproblems-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-xu-li-modifiedinertialhybridandshrinkingprojectionalgorithmsforsolvingfixedpointproblems-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TXL_MATH20,\nauthor={Tan, Bing and Xu, Shanshan and Li, Songxiao},\ntitle={Modified inertial hybrid and shrinking projection algorithms for solving fixed point problems},\njournal={Mathematics},\nyear={2020},\nvolume={8},\nnumber={2},\ndoi={10.3390/math8020236},\npages={236},\nurl={https://bingtan.me/files/paper/TXL-Math2020.pdf},\nabstract={In this paper, we introduce two modified inertial hybrid and shrinking projection algorithms for solving fixed point problems by combining the modified inertial Mann algorithm with the projection algorithm. We establish strong convergence theorems under certain suitable conditions. Finally, our algorithms are applied to convex feasibility problem, variational inequality problem, and location theory. The algorithms and results presented in this paper can summarize and unify corresponding results previously known in this field.},\nkeywords={Conjugate gradient method,  Hybrid projection method,  Inertial method,  Nonexpansive mapping,  Shrinking projection method,  Hybrid steepest descent method,  Strong convergence},\nabbrev_source_title={Mathematics},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we introduce two modified inertial hybrid and shrinking projection algorithms for solving fixed point problems by combining the modified inertial Mann algorithm with the projection algorithm. We establish strong convergence theorems under certain suitable conditions. Finally, our algorithms are applied to convex feasibility problem, variational inequality problem, and location theory. The algorithms and results presented in this paper can summarize and unify corresponding results previously known in this field.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-zhou-li-strongconvergenceofmodifiedinertialmannalgorithmsfornonexpansivemappings-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Zhou, Z.;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Strong convergence of modified inertial mann algorithms for nonexpansive mappings.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Mathematics</i>, 8(4): 462.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TZL-Math2020.pdf\"\n     onclick=\"log_download('tan-zhou-li-strongconvergenceofmodifiedinertialmannalgorithmsfornonexpansivemappings-2020', 'https://bingtan.me/files/paper/TZL-Math2020.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Strong convergence of modified inertial mann algorithms for nonexpansive mappings [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.3390/math8040462\"\n     onclick=\"log_download('tan-zhou-li-strongconvergenceofmodifiedinertialmannalgorithmsfornonexpansivemappings-2020', 'http://doi.org/10.3390/math8040462', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-zhou-li-strongconvergenceofmodifiedinertialmannalgorithmsfornonexpansivemappings-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-zhou-li-strongconvergenceofmodifiedinertialmannalgorithmsfornonexpansivemappings-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TZL_MATH20,\nauthor={Tan, Bing and Zhou, Zheng and Li, Songxiao},\ntitle={Strong convergence of modified inertial mann algorithms for nonexpansive mappings},\njournal={Mathematics},\nyear={2020},\nvolume={8},\nnumber={4},\ndoi={10.3390/math8040462},\npages={462},\nurl={https://bingtan.me/files/paper/TZL-Math2020.pdf},\nabstract={We investigated two new modified inertial Mann Halpern and inertial Mann viscosity algorithms for solving fixed point problems. Strong convergence theorems under some fewer restricted conditions are established in the framework of infinite dimensional Hilbert spaces. Finally, some numerical examples are provided to support our main results. The algorithms and results presented in this paper can generalize and extend corresponding results previously known in the literature.},\nkeywords={Halpern method,  Inertial method,  Nonexpansive mapping,  Strong convergence,  Viscosity method},\nabbrev_source_title={Mathematics},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We investigated two new modified inertial Mann Halpern and inertial Mann viscosity algorithms for solving fixed point problems. Strong convergence theorems under some fewer restricted conditions are established in the framework of infinite dimensional Hilbert spaces. Finally, some numerical examples are provided to support our main results. The algorithms and results presented in this paper can generalize and extend corresponding results previously known in the literature.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"liu-tan-cho-ontheresolutionofvariationalinequalityproblemswithadoublehierarchicalstructure-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Liu, L.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Cho, S. Y.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  On the resolution of variational inequality problems with a double-hierarchical structure.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Nonlinear and Convex Analysis</i>, 21(2): 377–386.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><span style=\"color: red\">(ESI Highly Cited Paper)</span></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/LTC-JNCA2020.pdf\"\n     onclick=\"log_download('liu-tan-cho-ontheresolutionofvariationalinequalityproblemswithadoublehierarchicalstructure-2020', 'https://bingtan.me/files/paper/LTC-JNCA2020.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"On the resolution of variational inequality problems with a double-hierarchical structure [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/liu-tan-cho-ontheresolutionofvariationalinequalityproblemswithadoublehierarchicalstructure-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('liu-tan-cho-ontheresolutionofvariationalinequalityproblemswithadoublehierarchicalstructure-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{LTC_JNCA20,\nauthor={Liu, Liya and Tan, Bing and Cho, Sun Y.},\ntitle={On the resolution of variational inequality problems with a double-hierarchical structure},\njournal={Journal of Nonlinear and Convex Analysis},\nyear={2020},\nvolume={21},\nnumber={2},\npages={377--386},\nurl={https://bingtan.me/files/paper/LTC-JNCA2020.pdf},\nabstract={In this paper, we discuss a pseudo-monotone variational inequality problem with a variational inequality constraint over a general, nonempty, closed and convex set, which is called the double-hierarchical constrained optimization problem. In addition, we propose an iterative algorithm by incorporating inertial terms in the extragradient algorithm. Strong convergence of the algorithm to the unique solution of the problem is guaranteed under certain assumptions.},\nkeywords={Constrained optimization problem,  Inertial method, Pseudomonotone operator,  Variational inequality problem},\nabbrev_source_title={J. Nonlinear Convex Anal.},\nbibbase_note={&lt;span style=&quot;color: red&quot;&gt;(ESI Highly Cited Paper)&lt;/span&gt;},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we discuss a pseudo-monotone variational inequality problem with a variational inequality constraint over a general, nonempty, closed and convex set, which is called the double-hierarchical constrained optimization problem. In addition, we propose an iterative algorithm by incorporating inertial terms in the extragradient algorithm. Strong convergence of the algorithm to the unique solution of the problem is guaranteed under certain assumptions.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"zhou-tan-li-anewacceleratedselfadaptivestepsizealgorithmwithexcellentstabilityforsplitcommonfixedpointproblems-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Zhou, Z.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  A new accelerated self-adaptive stepsize algorithm with excellent stability for split common fixed point problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Computational and Applied Mathematics</i>, 39(3): 220.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/ZTL-COAM2020.pdf\"\n     onclick=\"log_download('zhou-tan-li-anewacceleratedselfadaptivestepsizealgorithmwithexcellentstabilityforsplitcommonfixedpointproblems-2020', 'https://bingtan.me/files/paper/ZTL-COAM2020.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"A new accelerated self-adaptive stepsize algorithm with excellent stability for split common fixed point problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s40314-020-01237-0\"\n     onclick=\"log_download('zhou-tan-li-anewacceleratedselfadaptivestepsizealgorithmwithexcellentstabilityforsplitcommonfixedpointproblems-2020', 'http://doi.org/10.1007/s40314-020-01237-0', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/zhou-tan-li-anewacceleratedselfadaptivestepsizealgorithmwithexcellentstabilityforsplitcommonfixedpointproblems-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('zhou-tan-li-anewacceleratedselfadaptivestepsizealgorithmwithexcellentstabilityforsplitcommonfixedpointproblems-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{ZTL_COAM20,\nauthor={Zhou, Zheng and Tan, Bing and Li, Songxiao},\ntitle={A new accelerated self-adaptive stepsize algorithm with excellent stability for split common fixed point problems},\njournal={Computational and Applied Mathematics},\nyear={2020},\nvolume={39},\nnumber={3},\ndoi={10.1007/s40314-020-01237-0},\npages={220},\nurl={https://bingtan.me/files/paper/ZTL-COAM2020.pdf},\nabstract={In the framework of Hilbert spaces, we study the solutions of split common fixed point problems. A new accelerated self-adaptive stepsize algorithm with excellent stability is proposed under the effects of inertial techniques and Meir–Keeler contraction mappings. The strong convergence theorems are obtained without prior knowledge of operator norms. Finally, in applications, our main results in this paper are applied to signal recovery problems.},\nkeywords={Inertial method,  Meir–Keeler contraction,  Adaptive stepsize,  Signal processing problem, Split common fixed point problem},\nabbrev_source_title={Comput. Appl. Math.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In the framework of Hilbert spaces, we study the solutions of split common fixed point problems. A new accelerated self-adaptive stepsize algorithm with excellent stability is proposed under the effects of inertial techniques and Meir–Keeler contraction mappings. The strong convergence theorems are obtained without prior knowledge of operator norms. Finally, in applications, our main results in this paper are applied to signal recovery problems.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"zhou-tan-li-aninertialshrinkingprojectionalgorithmforsplitcommonfixedpointproblems-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Zhou, Z.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  An inertial shrinking projection algorithm for split common fixed point problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Applied Analysis and Computation</i>, 10(5): 2104–2120.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/ZTL-JAAC2020.pdf\"\n     onclick=\"log_download('zhou-tan-li-aninertialshrinkingprojectionalgorithmforsplitcommonfixedpointproblems-2020', 'https://bingtan.me/files/paper/ZTL-JAAC2020.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"An inertial shrinking projection algorithm for split common fixed point problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.11948/20190330\"\n     onclick=\"log_download('zhou-tan-li-aninertialshrinkingprojectionalgorithmforsplitcommonfixedpointproblems-2020', 'http://doi.org/10.11948/20190330', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/zhou-tan-li-aninertialshrinkingprojectionalgorithmforsplitcommonfixedpointproblems-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('zhou-tan-li-aninertialshrinkingprojectionalgorithmforsplitcommonfixedpointproblems-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{ZTL_JAAC20,\nauthor={Zhou, Zheng and Tan, Bing and Li, Songxiao},\ntitle={An inertial shrinking projection algorithm for split common fixed point problems},\njournal={Journal of Applied Analysis and Computation},\nyear={2020},\nvolume={10},\nnumber={5},\npages={2104--2120},\ndoi={10.11948/20190330},\nurl={https://bingtan.me/files/paper/ZTL-JAAC2020.pdf},\nabstract={In this paper, the purpose is to introduce and study a new modified shrinking projection algorithm with inertial effects, which solves split common fixed point problems in Banach spaces. The corresponding strong convergence theorems are obtained without the assumption of semi-compactness on map-pings. Finally, some numerical examples are presented to illustrate the results in this paper.},\nkeywords={Inertial method,  Shrinking projection method,  Split common fixed point problem,  Strong convergence},\nabbrev_source_title={J. Appl. Anal. Comput.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, the purpose is to introduce and study a new modified shrinking projection algorithm with inertial effects, which solves split common fixed point problems in Banach spaces. The corresponding strong convergence theorems are obtained without the assumption of semi-compactness on map-pings. Finally, some numerical examples are presented to illustrate the results in this paper.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"luo-shang-tan-ageneralinertialviscositytypemethodfornonexpansivemappingsanditsapplicationsinsignalprocessing-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Luo, Y.; Shang, M.;  and <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  A general inertial viscosity type method for nonexpansive mappings and its applications in signal processing.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Mathematics</i>, 8(2): 288.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/LST-Math2020.pdf\"\n     onclick=\"log_download('luo-shang-tan-ageneralinertialviscositytypemethodfornonexpansivemappingsanditsapplicationsinsignalprocessing-2020', 'https://bingtan.me/files/paper/LST-Math2020.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"A general inertial viscosity type method for nonexpansive mappings and its applications in signal processing [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.3390/math8020288\"\n     onclick=\"log_download('luo-shang-tan-ageneralinertialviscositytypemethodfornonexpansivemappingsanditsapplicationsinsignalprocessing-2020', 'http://doi.org/10.3390/math8020288', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/luo-shang-tan-ageneralinertialviscositytypemethodfornonexpansivemappingsanditsapplicationsinsignalprocessing-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('luo-shang-tan-ageneralinertialviscositytypemethodfornonexpansivemappingsanditsapplicationsinsignalprocessing-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{LST_MATH20,\nauthor={Luo, Yinglin and Shang, Meijuan and Tan, Bing},\ntitle={A general inertial viscosity type method for nonexpansive mappings and its applications in signal processing},\njournal={Mathematics},\nyear={2020},\nvolume={8},\nnumber={2},\ndoi={10.3390/math8020288},\npages={288},\nurl={https://bingtan.me/files/paper/LST-Math2020.pdf},\nabstract={In this paper, we propose viscosity algorithms with two different inertia parameters for solving fixed points of nonexpansive and strictly pseudocontractive mappings. Strong convergence theorems are obtained in Hilbert spaces and the applications to the signal processing are considered. Moreover, some numerical experiments of proposed algorithms and comparisons with existing algorithms are given to the demonstration of the efficiency of the proposed algorithms. The numerical results show that our algorithms are superior to some related algorithms.},\nkeywords={Inclusion problem,  Nonexpansive mapping,  Signal processing problem,  Strict pseudo-contraction,  Variational inequality problem},\nabbrev_source_title={Mathematics},\n}\n\n\n\n\n\n\n\n\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we propose viscosity algorithms with two different inertia parameters for solving fixed points of nonexpansive and strictly pseudocontractive mappings. Strong convergence theorems are obtained in Hilbert spaces and the applications to the signal processing are considered. Moreover, some numerical experiments of proposed algorithms and comparisons with existing algorithms are given to the demonstration of the efficiency of the proposed algorithms. The numerical results show that our algorithms are superior to some related algorithms.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_Wang__F_\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_Wang__F_')\"\n      onkeypress=\"toggleGroup('group_Wang__F_')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>Wang, F.</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"hu-wang-tan-wang-inertialiterativemethodforsolvingvariationalinequalityproblemsofpseudomonotoneoperatorsandfixedpointproblemsofnonexpansivemappingsinhilbertspaces-2023\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Hu, S.; Wang, Y.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Wang, F.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Inertial iterative method for solving variational inequality problems of pseudo-monotone operators and fixed point problems of nonexpansive mappings in Hilbert spaces.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Industrial and Management Optimization</i>, 19(4): 2655–2675.  2023.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/HWTW-JIMO2023.pdf\"\n     onclick=\"log_download('hu-wang-tan-wang-inertialiterativemethodforsolvingvariationalinequalityproblemsofpseudomonotoneoperatorsandfixedpointproblemsofnonexpansivemappingsinhilbertspaces-2023', 'https://bingtan.me/files/paper/HWTW-JIMO2023.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Inertial iterative method for solving variational inequality problems of pseudo-monotone operators and fixed point problems of nonexpansive mappings in Hilbert spaces [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.3934/jimo.2022060\"\n     onclick=\"log_download('hu-wang-tan-wang-inertialiterativemethodforsolvingvariationalinequalityproblemsofpseudomonotoneoperatorsandfixedpointproblemsofnonexpansivemappingsinhilbertspaces-2023', 'http://doi.org/10.3934/jimo.2022060', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/hu-wang-tan-wang-inertialiterativemethodforsolvingvariationalinequalityproblemsofpseudomonotoneoperatorsandfixedpointproblemsofnonexpansivemappingsinhilbertspaces-2023\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('hu-wang-tan-wang-inertialiterativemethodforsolvingvariationalinequalityproblemsofpseudomonotoneoperatorsandfixedpointproblemsofnonexpansivemappingsinhilbertspaces-2023')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{HWTW_JIMO23,\nauthor={Hu, Shaotao and Wang, Yuanheng and Tan, Bing and Wang, Fenghui},\ntitle={Inertial iterative method for solving variational inequality problems of pseudo-monotone operators and fixed point problems of nonexpansive mappings in {H}ilbert spaces},\njournal={Journal of Industrial and Management Optimization},\nyear={2023},\nvolume={19},\nnumber={4},\npages={2655--2675},\ndoi={10.3934/jimo.2022060},\nurl={https://bingtan.me/files/paper/HWTW-JIMO2023.pdf},\nabstract={In this paper, we propose a new inertial viscosity iterative algorithm for solving the variational inequality problem with a pseudo-monotone operator and the fixed point problem involving a nonexpansive mapping in real Hilbert spaces. The advantage of the proposed algorithm is that it can work without the prior knowledge of the Lipschitz constant of the mapping. The strong convergence of the sequence generated by the proposed algorithm is proved under some suitable assumptions imposed on the parameters. Some numerical experiments are given to support our main results.},\nkeywords={Inertial method,  Viscosity method,  Strong convergence, Variational inequality problem, Fixed point problem, Nonexpansive mapping, Pseudomonotone operator},\nabbrev_source_title={J. Ind. Manag. Optim.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we propose a new inertial viscosity iterative algorithm for solving the variational inequality problem with a pseudo-monotone operator and the fixed point problem involving a nonexpansive mapping in real Hilbert spaces. The advantage of the proposed algorithm is that it can work without the prior knowledge of the Lipschitz constant of the mapping. The strong convergence of the sequence generated by the proposed algorithm is proved under some suitable assumptions imposed on the parameters. Some numerical experiments are given to support our main results.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_Wang__X_\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_Wang__X_')\"\n      onkeypress=\"toggleGroup('group_Wang__X_')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>Wang, X.</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"tan-qin-wang-alternatedinertialalgorithmsforsplitfeasibilityproblems-2024\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Qin, X.;  and Wang, X.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Alternated inertial algorithms for split feasibility problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Numerical Algorithms</i>, 95(2): 773–812.  2024.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TQW-NUMA2024.pdf\"\n     onclick=\"log_download('tan-qin-wang-alternatedinertialalgorithmsforsplitfeasibilityproblems-2024', 'https://bingtan.me/files/paper/TQW-NUMA2024.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Alternated inertial algorithms for split feasibility problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s11075-023-01589-8\"\n     onclick=\"log_download('tan-qin-wang-alternatedinertialalgorithmsforsplitfeasibilityproblems-2024', 'http://doi.org/10.1007/s11075-023-01589-8', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-qin-wang-alternatedinertialalgorithmsforsplitfeasibilityproblems-2024\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-qin-wang-alternatedinertialalgorithmsforsplitfeasibilityproblems-2024')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TQW_NUMA24,\nauthor={Tan, Bing and Qin, Xiaolong and Wang, Xianfu},\ntitle={Alternated inertial algorithms for split feasibility problems},\njournal={Numerical Algorithms},\nyear={2024},\nvolume={95},\nnumber={2},\npages={773--812},\ndoi={10.1007/s11075-023-01589-8},\nurl={https://bingtan.me/files/paper/TQW-NUMA2024.pdf},\nabstract={We introduce four novel relaxed CQ algorithms with alternating inertial for solving split feasibility problems in real Hilbert spaces. The proposed algorithms employ a new non-monotonic adaptive step size criterion and utilize two different step sizes in each iteration. The weak convergence of the iterative sequences generated by the proposed algorithms is established under some weak conditions. Moreover, the Fejér monotonicity of the even subsequence with respect to the solution set is recovered. Two applications in signal denoising and image deblurring are given to illustrate the computational efficiency of our algorithms.},\nkeywords={Split feasibility problem,  CQ method,  Projection and contraction method,  Alternated inertial method,  Signal processing,  Image restoration},\nabbrev_source_title={Numer. Algorithms},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We introduce four novel relaxed CQ algorithms with alternating inertial for solving split feasibility problems in real Hilbert spaces. The proposed algorithms employ a new non-monotonic adaptive step size criterion and utilize two different step sizes in each iteration. The weak convergence of the iterative sequences generated by the proposed algorithms is established under some weak conditions. Moreover, the Fejér monotonicity of the even subsequence with respect to the solution set is recovered. Two applications in signal denoising and image deblurring are given to illustrate the computational efficiency of our algorithms.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_Wang__Y_\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_Wang__Y_')\"\n      onkeypress=\"toggleGroup('group_Wang__Y_')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>Wang, Y.</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"hu-wang-tan-wang-inertialiterativemethodforsolvingvariationalinequalityproblemsofpseudomonotoneoperatorsandfixedpointproblemsofnonexpansivemappingsinhilbertspaces-2023\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Hu, S.; Wang, Y.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Wang, F.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Inertial iterative method for solving variational inequality problems of pseudo-monotone operators and fixed point problems of nonexpansive mappings in Hilbert spaces.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Industrial and Management Optimization</i>, 19(4): 2655–2675.  2023.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/HWTW-JIMO2023.pdf\"\n     onclick=\"log_download('hu-wang-tan-wang-inertialiterativemethodforsolvingvariationalinequalityproblemsofpseudomonotoneoperatorsandfixedpointproblemsofnonexpansivemappingsinhilbertspaces-2023', 'https://bingtan.me/files/paper/HWTW-JIMO2023.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Inertial iterative method for solving variational inequality problems of pseudo-monotone operators and fixed point problems of nonexpansive mappings in Hilbert spaces [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.3934/jimo.2022060\"\n     onclick=\"log_download('hu-wang-tan-wang-inertialiterativemethodforsolvingvariationalinequalityproblemsofpseudomonotoneoperatorsandfixedpointproblemsofnonexpansivemappingsinhilbertspaces-2023', 'http://doi.org/10.3934/jimo.2022060', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/hu-wang-tan-wang-inertialiterativemethodforsolvingvariationalinequalityproblemsofpseudomonotoneoperatorsandfixedpointproblemsofnonexpansivemappingsinhilbertspaces-2023\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('hu-wang-tan-wang-inertialiterativemethodforsolvingvariationalinequalityproblemsofpseudomonotoneoperatorsandfixedpointproblemsofnonexpansivemappingsinhilbertspaces-2023')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{HWTW_JIMO23,\nauthor={Hu, Shaotao and Wang, Yuanheng and Tan, Bing and Wang, Fenghui},\ntitle={Inertial iterative method for solving variational inequality problems of pseudo-monotone operators and fixed point problems of nonexpansive mappings in {H}ilbert spaces},\njournal={Journal of Industrial and Management Optimization},\nyear={2023},\nvolume={19},\nnumber={4},\npages={2655--2675},\ndoi={10.3934/jimo.2022060},\nurl={https://bingtan.me/files/paper/HWTW-JIMO2023.pdf},\nabstract={In this paper, we propose a new inertial viscosity iterative algorithm for solving the variational inequality problem with a pseudo-monotone operator and the fixed point problem involving a nonexpansive mapping in real Hilbert spaces. The advantage of the proposed algorithm is that it can work without the prior knowledge of the Lipschitz constant of the mapping. The strong convergence of the sequence generated by the proposed algorithm is proved under some suitable assumptions imposed on the parameters. Some numerical experiments are given to support our main results.},\nkeywords={Inertial method,  Viscosity method,  Strong convergence, Variational inequality problem, Fixed point problem, Nonexpansive mapping, Pseudomonotone operator},\nabbrev_source_title={J. Ind. Manag. Optim.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we propose a new inertial viscosity iterative algorithm for solving the variational inequality problem with a pseudo-monotone operator and the fixed point problem involving a nonexpansive mapping in real Hilbert spaces. The advantage of the proposed algorithm is that it can work without the prior knowledge of the Lipschitz constant of the mapping. The strong convergence of the sequence generated by the proposed algorithm is proved under some suitable assumptions imposed on the parameters. Some numerical experiments are given to support our main results.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_Xie__Z_\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_Xie__Z_')\"\n      onkeypress=\"toggleGroup('group_Xie__Z_')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>Xie, Z.</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"xie-cai-tan-inertialsubgradientextragradientmethodforsolvingpseudomonotoneequilibriumprobelmsandfixedpointproblemsinhilbertspaces-2024\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Xie, Z.; Cai, G.;  and <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Inertial subgradient extragradient method for solving pseudomonotone equilibrium probelms and fixed point problems in Hilbert spaces.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Optimization</i>, 73(5): 1329-1354.  2024.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/XCT-OPT2024.pdf\"\n     onclick=\"log_download('xie-cai-tan-inertialsubgradientextragradientmethodforsolvingpseudomonotoneequilibriumprobelmsandfixedpointproblemsinhilbertspaces-2024', 'https://bingtan.me/files/paper/XCT-OPT2024.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Inertial subgradient extragradient method for solving pseudomonotone equilibrium probelms and fixed point problems in Hilbert spaces [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1080/02331934.2022.2157677\"\n     onclick=\"log_download('xie-cai-tan-inertialsubgradientextragradientmethodforsolvingpseudomonotoneequilibriumprobelmsandfixedpointproblemsinhilbertspaces-2024', 'http://doi.org/10.1080/02331934.2022.2157677', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/xie-cai-tan-inertialsubgradientextragradientmethodforsolvingpseudomonotoneequilibriumprobelmsandfixedpointproblemsinhilbertspaces-2024\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('xie-cai-tan-inertialsubgradientextragradientmethodforsolvingpseudomonotoneequilibriumprobelmsandfixedpointproblemsinhilbertspaces-2024')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{XCT_OPT24,\nauthor={Xie, Zhongbing and Cai, Gang and Tan, Bing},\ntitle={Inertial subgradient extragradient method for solving pseudomonotone equilibrium probelms and fixed point problems in Hilbert spaces},\njournal={Optimization},\nyear={2024},\nvolume={73},\nnumber={5},\npages={1329-1354},\ndoi={10.1080/02331934.2022.2157677},\nurl={https://bingtan.me/files/paper/XCT-OPT2024.pdf},\nabstract={This paper proposes a new inertial subgradient extragradient method for solving equilibrium problems with pseudomonotone and Lipschitz-type bifunctions and fixed point problems for nonexpansive mappings in real Hilbert spaces. Precisely, we prove that the sequence generated by proposed algorithm converges strongly to a common solution of equilibrium problems and fixed point problems. We use an effective self-adaptive step size rule to accelerate the convergence process of our proposed iterative algorithm. Moreover, some numerical results are given to show the effectiveness of the proposed algorithm. The results obtained in this paper extend and improve many recent ones in the literature.},\nkeywords={Inertial method,  Subgradient extragradient method, Equilibrium probelm, Fixed point problem, Strong convergence},\nabbrev_source_title={Optimization},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This paper proposes a new inertial subgradient extragradient method for solving equilibrium problems with pseudomonotone and Lipschitz-type bifunctions and fixed point problems for nonexpansive mappings in real Hilbert spaces. Precisely, we prove that the sequence generated by proposed algorithm converges strongly to a common solution of equilibrium problems and fixed point problems. We use an effective self-adaptive step size rule to accelerate the convergence process of our proposed iterative algorithm. Moreover, some numerical results are given to show the effectiveness of the proposed algorithm. The results obtained in this paper extend and improve many recent ones in the literature.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_Xu__S_\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_Xu__S_')\"\n      onkeypress=\"toggleGroup('group_Xu__S_')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>Xu, S.</span>\n      <span class=\"bibbase_group_count\">\n        \n        (4)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"tan-xu-strongconvergenceoftwoinertialprojectionalgorithmsinhilbertspaces-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Xu, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Strong convergence of two inertial projection algorithms in Hilbert spaces.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Applied and Numerical Optimization</i>, 2(2): 171–186.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TX-JANO2020.pdf\"\n     onclick=\"log_download('tan-xu-strongconvergenceoftwoinertialprojectionalgorithmsinhilbertspaces-2020', 'https://bingtan.me/files/paper/TX-JANO2020.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Strong convergence of two inertial projection algorithms in Hilbert spaces [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.23952/jano.2.2020.2.04\"\n     onclick=\"log_download('tan-xu-strongconvergenceoftwoinertialprojectionalgorithmsinhilbertspaces-2020', 'http://doi.org/10.23952/jano.2.2020.2.04', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-xu-strongconvergenceoftwoinertialprojectionalgorithmsinhilbertspaces-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-xu-strongconvergenceoftwoinertialprojectionalgorithmsinhilbertspaces-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TX_JANO20,\nauthor={Tan, Bing and Xu, Shanshan},\ntitle={Strong convergence of two inertial projection algorithms in {H}ilbert spaces},\njournal={Journal of Applied and Numerical Optimization},\nyear={2020},\nvolume={2},\nnumber={2},\npages={171--186},\ndoi={10.23952/jano.2.2020.2.04},\nurl={https://bingtan.me/files/paper/TX-JANO2020.pdf},\nabstract={In this paper, we propose two inertial projection algorithms for finding a common solution of monotone variational inclusions and hierarchical fixed point problems of nonexpansive mappings. We obtain two strong convergence theorems under some suitable conditions in Hilbert spaces. In addition, we also give numerical examples to compare our algorithms with the existing ones. Numerical results show that our proposed algorithms are efficient and robust.},\nkeywords={Hierarchical fixed point problem,  Inertial method,  Monotone operator,  Strong convergence,  Inclusion problem},\nabbrev_source_title={J. Appl. Numer. Optim.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we propose two inertial projection algorithms for finding a common solution of monotone variational inclusions and hierarchical fixed point problems of nonexpansive mappings. We obtain two strong convergence theorems under some suitable conditions in Hilbert spaces. In addition, we also give numerical examples to compare our algorithms with the existing ones. Numerical results show that our proposed algorithms are efficient and robust.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-xu-li-inertialshrinkingprojectionalgorithmsforsolvinghierarchicalvariationalinequalityproblems-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Xu, S.;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Inertial shrinking projection algorithms for solving hierarchical variational inequality problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Nonlinear and Convex Analysis</i>, 21(4): 871–884.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><span style=\"color: red\">(<s>ESI Highly Cited Paper</s>)</span></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TXL-JNCA2020.pdf\"\n     onclick=\"log_download('tan-xu-li-inertialshrinkingprojectionalgorithmsforsolvinghierarchicalvariationalinequalityproblems-2020', 'https://bingtan.me/files/paper/TXL-JNCA2020.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Inertial shrinking projection algorithms for solving hierarchical variational inequality problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-xu-li-inertialshrinkingprojectionalgorithmsforsolvinghierarchicalvariationalinequalityproblems-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-xu-li-inertialshrinkingprojectionalgorithmsforsolvinghierarchicalvariationalinequalityproblems-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TXL_JNCA20_2,\nauthor={Tan, Bing and Xu, Shanshan and Li, Songxiao},\ntitle={Inertial shrinking projection algorithms for solving hierarchical variational inequality problems},\njournal={Journal of Nonlinear and Convex Analysis},\nyear={2020},\nvolume={21},\nnumber={4},\npages={871--884},\nurl={https://bingtan.me/files/paper/TXL-JNCA2020.pdf},\nabstract={In this paper, we propose two inertial shrinking algorithms to approximate a solution of hierarchical variational inequality problems with nonex-pansive mappings in Hilbert spaces. We prove strong convergence theorems under some mild conditions. Finally, we present some numerical examples to compare our algorithms with some existing algorithms, which illustrate the advantage of our proposed algorithms.},\nkeywords={Hierarchical variational inequality problem,  Inertial method, Mann method,  Nonexpansive mapping,  Shrinking projection method,  Strong convergence},\nabbrev_source_title={J. Nonlinear Convex Anal.},\nbibbase_note={&lt;span style=&quot;color: red&quot;&gt;(&lt;s&gt;ESI Highly Cited Paper&lt;/s&gt;)&lt;/span&gt;},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we propose two inertial shrinking algorithms to approximate a solution of hierarchical variational inequality problems with nonex-pansive mappings in Hilbert spaces. We prove strong convergence theorems under some mild conditions. Finally, we present some numerical examples to compare our algorithms with some existing algorithms, which illustrate the advantage of our proposed algorithms.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-xu-li-inertialhybridandshrinkingprojectionalgorithmsforsolvingvariationalinequalityproblems-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Xu, S.;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Inertial hybrid and shrinking projection algorithms for solving variational inequality problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Nonlinear and Convex Analysis</i>, 21(10): 2193–2206.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TXL-JNCA2020-10.pdf\"\n     onclick=\"log_download('tan-xu-li-inertialhybridandshrinkingprojectionalgorithmsforsolvingvariationalinequalityproblems-2020', 'https://bingtan.me/files/paper/TXL-JNCA2020-10.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Inertial hybrid and shrinking projection algorithms for solving variational inequality problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-xu-li-inertialhybridandshrinkingprojectionalgorithmsforsolvingvariationalinequalityproblems-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-xu-li-inertialhybridandshrinkingprojectionalgorithmsforsolvingvariationalinequalityproblems-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TXL_JNCA20_1,\nauthor={Tan, Bing and Xu, Shanshan and Li, Songxiao},\ntitle={Inertial hybrid and shrinking projection algorithms for solving variational inequality problems},\njournal={Journal of Nonlinear and Convex Analysis},\nyear={2020},\nvolume={21},\nnumber={10},\npages={2193--2206},\nurl={https://bingtan.me/files/paper/TXL-JNCA2020-10.pdf},\nabstract={In this paper, we propose two inertial hybrid and shrinking projection algorithms for strict pseudo-contractions in Hilbert spaces and obtain strong theorems in general conditions. In addition, we also propose two new inertial hybrid and shrinking projection algorithms without extrapolating step for non-expansive mappings in Hilbert spaces and get strong convergence results. Finally, we give some numerical examples to illustrate the computational performance of our proposed algorithms.},\nkeywords={Variational inequality problem,  Inertial method, Hybrid projection method, Shrinking projection method, Strong convergence},\nabbrev_source_title={J. Nonlinear Convex Anal.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we propose two inertial hybrid and shrinking projection algorithms for strict pseudo-contractions in Hilbert spaces and obtain strong theorems in general conditions. In addition, we also propose two new inertial hybrid and shrinking projection algorithms without extrapolating step for non-expansive mappings in Hilbert spaces and get strong convergence results. Finally, we give some numerical examples to illustrate the computational performance of our proposed algorithms.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-xu-li-modifiedinertialhybridandshrinkingprojectionalgorithmsforsolvingfixedpointproblems-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Xu, S.;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Modified inertial hybrid and shrinking projection algorithms for solving fixed point problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Mathematics</i>, 8(2): 236.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TXL-Math2020.pdf\"\n     onclick=\"log_download('tan-xu-li-modifiedinertialhybridandshrinkingprojectionalgorithmsforsolvingfixedpointproblems-2020', 'https://bingtan.me/files/paper/TXL-Math2020.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Modified inertial hybrid and shrinking projection algorithms for solving fixed point problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.3390/math8020236\"\n     onclick=\"log_download('tan-xu-li-modifiedinertialhybridandshrinkingprojectionalgorithmsforsolvingfixedpointproblems-2020', 'http://doi.org/10.3390/math8020236', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-xu-li-modifiedinertialhybridandshrinkingprojectionalgorithmsforsolvingfixedpointproblems-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-xu-li-modifiedinertialhybridandshrinkingprojectionalgorithmsforsolvingfixedpointproblems-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TXL_MATH20,\nauthor={Tan, Bing and Xu, Shanshan and Li, Songxiao},\ntitle={Modified inertial hybrid and shrinking projection algorithms for solving fixed point problems},\njournal={Mathematics},\nyear={2020},\nvolume={8},\nnumber={2},\ndoi={10.3390/math8020236},\npages={236},\nurl={https://bingtan.me/files/paper/TXL-Math2020.pdf},\nabstract={In this paper, we introduce two modified inertial hybrid and shrinking projection algorithms for solving fixed point problems by combining the modified inertial Mann algorithm with the projection algorithm. We establish strong convergence theorems under certain suitable conditions. Finally, our algorithms are applied to convex feasibility problem, variational inequality problem, and location theory. The algorithms and results presented in this paper can summarize and unify corresponding results previously known in this field.},\nkeywords={Conjugate gradient method,  Hybrid projection method,  Inertial method,  Nonexpansive mapping,  Shrinking projection method,  Hybrid steepest descent method,  Strong convergence},\nabbrev_source_title={Mathematics},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we introduce two modified inertial hybrid and shrinking projection algorithms for solving fixed point problems by combining the modified inertial Mann algorithm with the projection algorithm. We establish strong convergence theorems under certain suitable conditions. Finally, our algorithms are applied to convex feasibility problem, variational inequality problem, and location theory. The algorithms and results presented in this paper can summarize and unify corresponding results previously known in this field.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_Yao__J_\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_Yao__J_')\"\n      onkeypress=\"toggleGroup('group_Yao__J_')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>Yao, J.</span>\n      <span class=\"bibbase_group_count\">\n        \n        (5)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"tan-qin-yao-strongconvergenceofinertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalitieswithapplicationstooptimalcontrolproblems-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Qin, X.;  and Yao, J. C.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Strong convergence of inertial projection and contraction methods for pseudomonotone variational inequalities with applications to optimal control problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Global Optimization</i>, 82(3): 523–557.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TQY-JOGO2022.pdf\"\n     onclick=\"log_download('tan-qin-yao-strongconvergenceofinertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalitieswithapplicationstooptimalcontrolproblems-2022', 'https://bingtan.me/files/paper/TQY-JOGO2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Strong convergence of inertial projection and contraction methods for pseudomonotone variational inequalities with applications to optimal control problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s10898-021-01095-y\"\n     onclick=\"log_download('tan-qin-yao-strongconvergenceofinertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalitieswithapplicationstooptimalcontrolproblems-2022', 'http://doi.org/10.1007/s10898-021-01095-y', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-qin-yao-strongconvergenceofinertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalitieswithapplicationstooptimalcontrolproblems-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-qin-yao-strongconvergenceofinertialprojectionandcontractionmethodsforpseudomonotonevariationalinequalitieswithapplicationstooptimalcontrolproblems-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TQY_JOGO22,\nauthor={Tan, Bing and Qin, Xiaolong and Yao, Jen C.},\ntitle={Strong convergence of inertial projection and contraction methods for pseudomonotone variational inequalities with applications to optimal control problems},\njournal={Journal of Global Optimization},\nyear={2022},\nvolume={82},\nnumber={3},\npages={523--557},\ndoi={10.1007/s10898-021-01095-y},\nurl={https://bingtan.me/files/paper/TQY-JOGO2022.pdf},\nabstract={This paper investigates some inertial projection and contraction methods for solving pseudomonotone variational inequality problems in real Hilbert spaces. The algorithms use a new non-monotonic step size so that they can work without the prior knowledge of the Lipschitz constant of the operator. Strong convergence theorems of the suggested algorithms are obtained under some suitable conditions. Some numerical experiments in finite- and infinite-dimensional spaces and applications in optimal control problems are implemented to demonstrate the performance of the suggested schemes and we also compare them with several related results.},\nkeywords={Inertial method,  Optimal control problem,  Projection and contraction method,  Pseudomonotone operator,  Subgradient extragradient method,  Variational inequality problem},\nabbrev_source_title={J. Global Optim.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This paper investigates some inertial projection and contraction methods for solving pseudomonotone variational inequality problems in real Hilbert spaces. The algorithms use a new non-monotonic step size so that they can work without the prior knowledge of the Lipschitz constant of the operator. Strong convergence theorems of the suggested algorithms are obtained under some suitable conditions. Some numerical experiments in finite- and infinite-dimensional spaces and applications in optimal control problems are implemented to demonstrate the performance of the suggested schemes and we also compare them with several related results.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-petruel-qin-yao-globalandlinearconvergenceofalternatedinertialsingleprojectionalgorithmsforpseudomonotonevariationalinequalities-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Petruşel, A.; Qin, X.;  and Yao, J. C.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Global and linear convergence of alternated inertial single projection algorithms for pseudo-monotone variational inequalities.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Fixed Point Theory</i>, 23(1): 391–426.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TPQY-FPT2022.pdf\"\n     onclick=\"log_download('tan-petruel-qin-yao-globalandlinearconvergenceofalternatedinertialsingleprojectionalgorithmsforpseudomonotonevariationalinequalities-2022', 'https://bingtan.me/files/paper/TPQY-FPT2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Global and linear convergence of alternated inertial single projection algorithms for pseudo-monotone variational inequalities [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.24193/fpt-ro.2022.1.25\"\n     onclick=\"log_download('tan-petruel-qin-yao-globalandlinearconvergenceofalternatedinertialsingleprojectionalgorithmsforpseudomonotonevariationalinequalities-2022', 'http://doi.org/10.24193/fpt-ro.2022.1.25', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-petruel-qin-yao-globalandlinearconvergenceofalternatedinertialsingleprojectionalgorithmsforpseudomonotonevariationalinequalities-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>2 downloads</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-petruel-qin-yao-globalandlinearconvergenceofalternatedinertialsingleprojectionalgorithmsforpseudomonotonevariationalinequalities-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TPQY_FPT22,\nauthor={Tan, Bing and Petruşel, Adrian and Qin, Xiaolong and Yao, Jen C.},\ntitle={Global and linear convergence of alternated inertial single projection algorithms for pseudo-monotone variational inequalities},\njournal={Fixed Point Theory},\nyear={2022},\nvolume={23},\nnumber={1},\npages={391--426},\ndoi={10.24193/fpt-ro.2022.1.25},\nurl={https://bingtan.me/files/paper/TPQY-FPT2022.pdf},\nabstract={In this paper, we investigate three new relaxed single projection methods with alternating inertial extrapolation steps and adaptive non-monotonic step sizes for solving pseudo-monotone variational inequalities in real Hilbert spaces. The proposed algorithms need to compute the projection on the feasible set only once in each iteration and they can work adaptively without the prior information of the Lipschitz constant of the mapping. The weak convergence theorems of the proposed iterative schemes are established under some appropriate conditions imposed on the parameters. These methods recover the Fejér monotonicity of the even subsequence with respect to the solution and obtain linear convergence rates. Finally, some numerical experiments and applications to optimal control problems are provided to demonstrate the advantages and efficiency of the proposed methods compared to some recent related ones.},\nkeywords={Adaptive stepsize,  Alternated inertial method,  Projection and contraction method,  Pseudomonotone operator,  Subgradient extragradient method,  Variational inequality problem},\nabbrev_source_title={Fixed Point Theory},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we investigate three new relaxed single projection methods with alternating inertial extrapolation steps and adaptive non-monotonic step sizes for solving pseudo-monotone variational inequalities in real Hilbert spaces. The proposed algorithms need to compute the projection on the feasible set only once in each iteration and they can work adaptively without the prior information of the Lipschitz constant of the mapping. The weak convergence theorems of the proposed iterative schemes are established under some appropriate conditions imposed on the parameters. These methods recover the Fejér monotonicity of the even subsequence with respect to the solution and obtain linear convergence rates. Finally, some numerical experiments and applications to optimal control problems are provided to demonstrate the advantages and efficiency of the proposed methods compared to some recent related ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-cho-yao-acceleratedinertialsubgradientextragradientalgorithmswithnonmonotonicstepsizesforequilibriumproblemsandfixedpointproblems-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Cho, S. Y.;  and Yao, J. C.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Accelerated inertial subgradient extragradient algorithms with non-monotonic step sizes for equilibrium problems and fixed point problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Nonlinear and Variational Analysis</i>, 6(1): 89–122.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TCY-JNVA2022.pdf\"\n     onclick=\"log_download('tan-cho-yao-acceleratedinertialsubgradientextragradientalgorithmswithnonmonotonicstepsizesforequilibriumproblemsandfixedpointproblems-2022', 'https://bingtan.me/files/paper/TCY-JNVA2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Accelerated inertial subgradient extragradient algorithms with non-monotonic step sizes for equilibrium problems and fixed point problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.23952/jnva.6.2022.1.06\"\n     onclick=\"log_download('tan-cho-yao-acceleratedinertialsubgradientextragradientalgorithmswithnonmonotonicstepsizesforequilibriumproblemsandfixedpointproblems-2022', 'http://doi.org/10.23952/jnva.6.2022.1.06', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-cho-yao-acceleratedinertialsubgradientextragradientalgorithmswithnonmonotonicstepsizesforequilibriumproblemsandfixedpointproblems-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-cho-yao-acceleratedinertialsubgradientextragradientalgorithmswithnonmonotonicstepsizesforequilibriumproblemsandfixedpointproblems-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TCY_JNVA22,\nauthor={Tan, Bing and Cho, Sun Y. and Yao, Jen C.},\ntitle={Accelerated inertial subgradient extragradient algorithms with non-monotonic step sizes for equilibrium problems and fixed point problems},\njournal={Journal of Nonlinear and Variational Analysis},\nyear={2022},\nvolume={6},\nnumber={1},\npages={89--122},\ndoi={10.23952/jnva.6.2022.1.06},\nurl={https://bingtan.me/files/paper/TCY-JNVA2022.pdf},\nabstract={This paper introduces several new accelerated subgradient extragradient methods with inertial effects for approximating a solution of a pseudomonotone equilibrium problem and a fixed point problem involving a quasi-nonexpansive mapping or a demicontractive mapping in real Hilbert spaces. The proposed algorithms use an adaptive non-monotonic step size criterion that does not include any Armijo line search process. Strong convergence theorems of the suggested iterative algorithms are established without the prior knowledge of the Lipschitz constants of the bifunction. Moreover, $R$-linear convergence is guaranteed under the assumption that the bifunction satisfies strong pseudomonotonicity. Applications to variational inequality problems are also considered. Finally, some numerical examples and applications, which demonstrate the advantages and efficiency of the proposed algorithms, are given.},\nkeywords={Equilibrium problem,  Fixed point problem,  Inertial method,  Pseudomonotone bifunction,  Subgradient extragradient method},\nabbrev_source_title={J. Nonlinear Var. Anal.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This paper introduces several new accelerated subgradient extragradient methods with inertial effects for approximating a solution of a pseudomonotone equilibrium problem and a fixed point problem involving a quasi-nonexpansive mapping or a demicontractive mapping in real Hilbert spaces. The proposed algorithms use an adaptive non-monotonic step size criterion that does not include any Armijo line search process. Strong convergence theorems of the suggested iterative algorithms are established without the prior knowledge of the Lipschitz constants of the bifunction. Moreover, $R$-linear convergence is guaranteed under the assumption that the bifunction satisfies strong pseudomonotonicity. Applications to variational inequality problems are also considered. Finally, some numerical examples and applications, which demonstrate the advantages and efficiency of the proposed algorithms, are given.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-qin-yao-strongconvergenceofselfadaptiveinertialalgorithmsforsolvingsplitvariationalinclusionproblemswithapplications-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Qin, X.;  and Yao, J. C.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Strong convergence of self-adaptive inertial algorithms for solving split variational inclusion problems with applications.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Scientific Computing</i>, 87(1): 20.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><span style=\"color: red\">(ESI Highly Cited Paper)</span></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TQY-JSC2021.pdf\"\n     onclick=\"log_download('tan-qin-yao-strongconvergenceofselfadaptiveinertialalgorithmsforsolvingsplitvariationalinclusionproblemswithapplications-2021', 'https://bingtan.me/files/paper/TQY-JSC2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Strong convergence of self-adaptive inertial algorithms for solving split variational inclusion problems with applications [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s10915-021-01428-9\"\n     onclick=\"log_download('tan-qin-yao-strongconvergenceofselfadaptiveinertialalgorithmsforsolvingsplitvariationalinclusionproblemswithapplications-2021', 'http://doi.org/10.1007/s10915-021-01428-9', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-qin-yao-strongconvergenceofselfadaptiveinertialalgorithmsforsolvingsplitvariationalinclusionproblemswithapplications-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-qin-yao-strongconvergenceofselfadaptiveinertialalgorithmsforsolvingsplitvariationalinclusionproblemswithapplications-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TQY_JSC21,\nauthor={Tan, Bing and Qin, Xiaolong and Yao, Jen C.},\ntitle={Strong convergence of self-adaptive inertial algorithms for solving split variational inclusion problems with applications},\njournal={Journal of Scientific Computing},\nyear={2021},\nvolume={87},\nnumber={1},\ndoi={10.1007/s10915-021-01428-9},\npages={20},\nurl={https://bingtan.me/files/paper/TQY-JSC2021.pdf},\nabstract={In this paper, four self-adaptive iterative algorithms with inertial effects are introduced to solve a split variational inclusion problem in real Hilbert spaces. One of the advantages of the suggested algorithms is that they can work without knowing the prior information of the operator norm. Strong convergence theorems of these algorithms are established under mild and standard assumptions. As applications, the split feasibility problem and the split minimization problem in real Hilbert spaces are studied. Finally, several preliminary numerical experiments as well as an example in the field of compressed sensing are proposed to support the advantages and efficiency of the suggested methods over some existing ones.},\nkeywords={Inertial method,  Mann method,  Signal processing problem,  Split variational inclusion problem,  Strong convergence,  Viscosity method},\nabbrev_source_title={J. Sci. Comput.},\nbibbase_note={&lt;span style=&quot;color: red&quot;&gt;(ESI Highly Cited Paper)&lt;/span&gt;},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, four self-adaptive iterative algorithms with inertial effects are introduced to solve a split variational inclusion problem in real Hilbert spaces. One of the advantages of the suggested algorithms is that they can work without knowing the prior information of the operator norm. Strong convergence theorems of these algorithms are established under mild and standard assumptions. As applications, the split feasibility problem and the split minimization problem in real Hilbert spaces are studied. Finally, several preliminary numerical experiments as well as an example in the field of compressed sensing are proposed to support the advantages and efficiency of the suggested methods over some existing ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-qin-yao-twomodifiedinertialprojectionalgorithmsforbilevelpseudomonotonevariationalinequalitieswithapplicationstooptimalcontrolproblems-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Qin, X.;  and Yao, J. C.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Two modified inertial projection algorithms for bilevel pseudomonotone variational inequalities with applications to optimal control problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Numerical Algorithms</i>, 88(4): 1757–1786.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TQY-NUMA2021.pdf\"\n     onclick=\"log_download('tan-qin-yao-twomodifiedinertialprojectionalgorithmsforbilevelpseudomonotonevariationalinequalitieswithapplicationstooptimalcontrolproblems-2021', 'https://bingtan.me/files/paper/TQY-NUMA2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Two modified inertial projection algorithms for bilevel pseudomonotone variational inequalities with applications to optimal control problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s11075-021-01093-x\"\n     onclick=\"log_download('tan-qin-yao-twomodifiedinertialprojectionalgorithmsforbilevelpseudomonotonevariationalinequalitieswithapplicationstooptimalcontrolproblems-2021', 'http://doi.org/10.1007/s11075-021-01093-x', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-qin-yao-twomodifiedinertialprojectionalgorithmsforbilevelpseudomonotonevariationalinequalitieswithapplicationstooptimalcontrolproblems-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-qin-yao-twomodifiedinertialprojectionalgorithmsforbilevelpseudomonotonevariationalinequalitieswithapplicationstooptimalcontrolproblems-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TQY_NUMA21,\nauthor={Tan, Bing and Qin, Xiaolong and Yao, Jen C.},\ntitle={Two modified inertial projection algorithms for bilevel pseudomonotone variational inequalities with applications to optimal control problems},\njournal={Numerical Algorithms},\nyear={2021},\nvolume={88},\nnumber={4},\npages={1757--1786},\ndoi={10.1007/s11075-021-01093-x},\nurl={https://bingtan.me/files/paper/TQY-NUMA2021.pdf},\nabstract={In this paper, we investigate two new algorithms for solving bilevel pseudomonotone variational inequality problems in real Hilbert spaces. The advantages of our algorithms are that they only need to calculate one projection on the feasible set in each iteration, and do not require the prior information of the Lipschitz constant of the cost operator. Furthermore, two new algorithms are derived to solve variational inequality problems. We establish the strong convergence of the proposed algorithms under some suitable conditions imposed on parameters. Finally, several numerical results and applications in optimal control problems are reported to illustrate the efficiency and advantages of the proposed algorithms.},\nkeywords={Bilevel variational inequality problem,  Hybrid steepest descent method,  Inertial extragradient method,  Projection and contraction method,  Pseudomonotone operator},\nabbrev_source_title={Numer. Algorithms},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we investigate two new algorithms for solving bilevel pseudomonotone variational inequality problems in real Hilbert spaces. The advantages of our algorithms are that they only need to calculate one projection on the feasible set in each iteration, and do not require the prior information of the Lipschitz constant of the cost operator. Furthermore, two new algorithms are derived to solve variational inequality problems. We establish the strong convergence of the proposed algorithms under some suitable conditions imposed on parameters. Finally, several numerical results and applications in optimal control problems are reported to illustrate the efficiency and advantages of the proposed algorithms.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_Zhou__X_\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_Zhou__X_')\"\n      onkeypress=\"toggleGroup('group_Zhou__X_')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>Zhou, X.</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"zhou-cai-tan-dong-amodifiedgeneralizedversionofprojectedreflectedgradientmethodinhilbertspaces-2023\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Zhou, X.; Cai, G.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Dong, Q. L.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  A modified generalized version of projected reflected gradient method in Hilbert spaces.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Numerical Algorithms</i>, doi:10.1007/s11075-023-01566-1.  2023.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/ZCTD-NUMA2023.pdf\"\n     onclick=\"log_download('zhou-cai-tan-dong-amodifiedgeneralizedversionofprojectedreflectedgradientmethodinhilbertspaces-2023', 'https://bingtan.me/files/paper/ZCTD-NUMA2023.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"A modified generalized version of projected reflected gradient method in Hilbert spaces [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s11075-023-01566-1\"\n     onclick=\"log_download('zhou-cai-tan-dong-amodifiedgeneralizedversionofprojectedreflectedgradientmethodinhilbertspaces-2023', 'http://doi.org/10.1007/s11075-023-01566-1', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/zhou-cai-tan-dong-amodifiedgeneralizedversionofprojectedreflectedgradientmethodinhilbertspaces-2023\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('zhou-cai-tan-dong-amodifiedgeneralizedversionofprojectedreflectedgradientmethodinhilbertspaces-2023')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{ZCTD_NUMA23,\nauthor={Zhou, Xiaolin and Cai, Gang and Tan, Bing and Dong, Qiao L.},\ntitle={A modified generalized version of projected reflected gradient method in Hilbert spaces},\njournal={Numerical Algorithms},\nyear={2023},\nvolume={doi:10.1007/s11075-023-01566-1},\ndoi={10.1007/s11075-023-01566-1},\nurl={https://bingtan.me/files/paper/ZCTD-NUMA2023.pdf},\nabstract={This article is concerned with a universal version of projected reflected gradient method with new step size for solving variational inequality problem in Hilbert spaces. Under appropriate assumptions controlled by the operators and parameters, we acquire the weak convergence of the proposed algorithm. We establish an R-linear convergence rate of our method on the condition that the relevant mapping is strongly monotone. We rework our first algorithm so that it can be simplified to several generalized methods in the literature. The efficacy and availability of our proposed iterative scheme are demonstrated in numerical experiments.},\nkeywords={Projected reflected gradient method, Variational inequality, Weak and linear convergence, Hilbert spaces},\nabbrev_source_title={Numer. Algorithms},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This article is concerned with a universal version of projected reflected gradient method with new step size for solving variational inequality problem in Hilbert spaces. Under appropriate assumptions controlled by the operators and parameters, we acquire the weak convergence of the proposed algorithm. We establish an R-linear convergence rate of our method on the condition that the relevant mapping is strongly monotone. We rework our first algorithm so that it can be simplified to several generalized methods in the literature. The efficacy and availability of our proposed iterative scheme are demonstrated in numerical experiments.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_Zhou__Z_\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_Zhou__Z_')\"\n      onkeypress=\"toggleGroup('group_Zhou__Z_')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>Zhou, Z.</span>\n      <span class=\"bibbase_group_count\">\n        \n        (10)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"zhou-tan-li-inertialalgorithmswithadaptivestepsizesforsplitvariationalinclusionproblemsandtheirapplicationstosignalrecoveryproblem-2023\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Zhou, Z.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Inertial algorithms with adaptive stepsizes for split variational inclusion problems and their applications to signal recovery problem.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Mathematical Methods in the Applied Sciences</i>, doi:10.1002/mma.9436.  2023.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/ZTL-MMAS2023.pdf\"\n     onclick=\"log_download('zhou-tan-li-inertialalgorithmswithadaptivestepsizesforsplitvariationalinclusionproblemsandtheirapplicationstosignalrecoveryproblem-2023', 'https://bingtan.me/files/paper/ZTL-MMAS2023.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Inertial algorithms with adaptive stepsizes for split variational inclusion problems and their applications to signal recovery problem [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1002/mma.9436\"\n     onclick=\"log_download('zhou-tan-li-inertialalgorithmswithadaptivestepsizesforsplitvariationalinclusionproblemsandtheirapplicationstosignalrecoveryproblem-2023', 'http://doi.org/10.1002/mma.9436', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/zhou-tan-li-inertialalgorithmswithadaptivestepsizesforsplitvariationalinclusionproblemsandtheirapplicationstosignalrecoveryproblem-2023\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('zhou-tan-li-inertialalgorithmswithadaptivestepsizesforsplitvariationalinclusionproblemsandtheirapplicationstosignalrecoveryproblem-2023')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{ZTL_MMAS23,\nauthor={Zhou, Zheng and Tan, Bing and Li, Songxiao},\ntitle={Inertial algorithms with adaptive stepsizes for split variational inclusion problems and their applications to signal recovery problem},\njournal={Mathematical Methods in the Applied Sciences},\nyear={2023},\nvolume={doi:10.1002/mma.9436},\ndoi={10.1002/mma.9436},\nurl={https://bingtan.me/files/paper/ZTL-MMAS2023.pdf},\nabstract={With the help of the Meir-Keeler contraction method and the Mann-type method, two adaptive inertial iterative schemes are introduced for finding solutions of the split variational inclusion problem in Hilbert spaces. The strong convergence of the suggested algorithms is guaranteed by a new stepsize criterion that does not require calculation of the bounded linear operator norm. Some numerical experiments and applications in signal recovery problems are given to demonstrate the efficiency of the proposed algorithms.},\nkeywords={Adaptive stepsize, Inertial method, Mann method, Meir-Keeler contraction, Signal recovery, Split variational inclusion problem},\nabbrev_source_title={Math. Methods Appl. Sci.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  With the help of the Meir-Keeler contraction method and the Mann-type method, two adaptive inertial iterative schemes are introduced for finding solutions of the split variational inclusion problem in Hilbert spaces. The strong convergence of the suggested algorithms is guaranteed by a new stepsize criterion that does not require calculation of the bounded linear operator norm. Some numerical experiments and applications in signal recovery problems are given to demonstrate the efficiency of the proposed algorithms.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-zhou-li-viscositytypeinertialextragradientalgorithmsforsolvingvariationalinequalityproblemsandfixedpointproblems-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Zhou, Z.;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Viscosity-type inertial extragradient algorithms for solving variational inequality problems and fixed point problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Applied Mathematics and Computing</i>, 68(2): 1387–1411.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TZL-JAMC2022.pdf\"\n     onclick=\"log_download('tan-zhou-li-viscositytypeinertialextragradientalgorithmsforsolvingvariationalinequalityproblemsandfixedpointproblems-2022', 'https://bingtan.me/files/paper/TZL-JAMC2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Viscosity-type inertial extragradient algorithms for solving variational inequality problems and fixed point problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s12190-021-01576-z\"\n     onclick=\"log_download('tan-zhou-li-viscositytypeinertialextragradientalgorithmsforsolvingvariationalinequalityproblemsandfixedpointproblems-2022', 'http://doi.org/10.1007/s12190-021-01576-z', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-zhou-li-viscositytypeinertialextragradientalgorithmsforsolvingvariationalinequalityproblemsandfixedpointproblems-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-zhou-li-viscositytypeinertialextragradientalgorithmsforsolvingvariationalinequalityproblemsandfixedpointproblems-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TZL_JAMC22,\nauthor={Tan, Bing and Zhou, Zheng and Li, Songxiao},\ntitle={Viscosity-type inertial extragradient algorithms for solving variational inequality problems and fixed point problems},\njournal={Journal of Applied Mathematics and Computing},\nyear={2022},\nvolume={68},\nnumber={2},\npages={1387--1411},\ndoi={10.1007/s12190-021-01576-z},\nurl={https://bingtan.me/files/paper/TZL-JAMC2022.pdf},\nabstract={The paper presents two inertial viscosity-type extragradient algorithms for finding a common solution of the variational inequality problem involving a monotone and Lipschitz continuous operator and of the fixed point problem with a demicontractive mapping in real Hilbert spaces. Our algorithms use a simple step size rule which is generated by some calculations at each iteration. Two strong convergence theorems are obtained without the prior knowledge of the Lipschitz constant of the operator. The numerical behaviors of the proposed algorithms in some numerical experiments are reported and compared with previously known ones.},\nkeywords={Fixed point problem,  Inertial method,  Subgradient extragradient method,  Tseng&#x27;s extragradient method,  Variational inequality problem},\nabbrev_source_title={J. Appl. Math. Comput.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  The paper presents two inertial viscosity-type extragradient algorithms for finding a common solution of the variational inequality problem involving a monotone and Lipschitz continuous operator and of the fixed point problem with a demicontractive mapping in real Hilbert spaces. Our algorithms use a simple step size rule which is generated by some calculations at each iteration. Two strong convergence theorems are obtained without the prior knowledge of the Lipschitz constant of the operator. The numerical behaviors of the proposed algorithms in some numerical experiments are reported and compared with previously known ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"zhou-tan-li-adaptivehybridsteepestdescentalgorithmsinvolvinganinertialextrapolationtermforsplitmonotonevariationalinclusionproblems-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Zhou, Z.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Adaptive hybrid steepest descent algorithms involving an inertial extrapolation term for split monotone variational inclusion problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Mathematical Methods in the Applied Sciences</i>, 45(15): 8835–8853.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/ZTL-MMAS2022.pdf\"\n     onclick=\"log_download('zhou-tan-li-adaptivehybridsteepestdescentalgorithmsinvolvinganinertialextrapolationtermforsplitmonotonevariationalinclusionproblems-2022', 'https://bingtan.me/files/paper/ZTL-MMAS2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Adaptive hybrid steepest descent algorithms involving an inertial extrapolation term for split monotone variational inclusion problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1002/mma.7931\"\n     onclick=\"log_download('zhou-tan-li-adaptivehybridsteepestdescentalgorithmsinvolvinganinertialextrapolationtermforsplitmonotonevariationalinclusionproblems-2022', 'http://doi.org/10.1002/mma.7931', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/zhou-tan-li-adaptivehybridsteepestdescentalgorithmsinvolvinganinertialextrapolationtermforsplitmonotonevariationalinclusionproblems-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>1 download</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('zhou-tan-li-adaptivehybridsteepestdescentalgorithmsinvolvinganinertialextrapolationtermforsplitmonotonevariationalinclusionproblems-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{ZTL_MMAS22,\nauthor={Zhou, Zheng and Tan, Bing and Li, Songxiao},\ntitle={Adaptive hybrid steepest descent algorithms involving an inertial extrapolation term for split monotone variational inclusion problems},\njournal={Mathematical Methods in the Applied Sciences},\nyear={2022},\nvolume={45},\nnumber={15},\npages={8835--8853},\ndoi={10.1002/mma.7931},\nurl={https://bingtan.me/files/paper/ZTL-MMAS2022.pdf},\nabstract={In this paper, we discuss the split monotone variational inclusion problem and propose two new inertial algorithms in infinite-dimensional Hilbert spaces. The iterative sequence by the proposed algorithms converges strongly to the solution of a certain variational inequality with the help of the hybrid steepest descent method. Furthermore, an adaptive step size criterion is considered in suggested algorithms to avoid the difficulty of calculating the operator norm. Meanwhile, our results are also applied to several other types of split problems. Finally, some numerical experiments show that our algorithms are realistic and summarize the known results.},\nkeywords={Adaptive stepsize,  Hybrid steepest descent method,  Inertial method,  Signal processing problem,  Strong convergence},\nabbrev_source_title={Math. Methods Appl. Sci.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we discuss the split monotone variational inclusion problem and propose two new inertial algorithms in infinite-dimensional Hilbert spaces. The iterative sequence by the proposed algorithms converges strongly to the solution of a certain variational inequality with the help of the hybrid steepest descent method. Furthermore, an adaptive step size criterion is considered in suggested algorithms to avoid the difficulty of calculating the operator norm. Meanwhile, our results are also applied to several other types of split problems. Finally, some numerical experiments show that our algorithms are realistic and summarize the known results.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"zhou-tan-cho-alternatedinertialsubgradientextragradientmethodsforsolvingvariationalinequalities-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Zhou, Z.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Cho, S. Y.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Alternated inertial subgradient extragradient methods for solving variational inequalities.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Nonlinear and Convex Analysis</i>, 23(11): 2593–2604.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/ZTC-JNCA2022.pdf\"\n     onclick=\"log_download('zhou-tan-cho-alternatedinertialsubgradientextragradientmethodsforsolvingvariationalinequalities-2022', 'https://bingtan.me/files/paper/ZTC-JNCA2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Alternated inertial subgradient extragradient methods for solving variational inequalities [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/zhou-tan-cho-alternatedinertialsubgradientextragradientmethodsforsolvingvariationalinequalities-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('zhou-tan-cho-alternatedinertialsubgradientextragradientmethodsforsolvingvariationalinequalities-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{ZTC_JNCA22,\nauthor={Zhou, Zheng and Tan, Bing and Cho, Sun Y.},\ntitle={Alternated inertial subgradient extragradient methods for solving variational inequalities},\njournal={Journal of Nonlinear and Convex Analysis},\nyear={2022},\nvolume={23},\nnumber={11},\npages={2593--2604},\nurl={https://bingtan.me/files/paper/ZTC-JNCA2022.pdf},\nabstract={The goal of this paper is to study some iterative algorithms for solving a pseudomonotone variational inequality in Hilbert spaces. The iterative algorithms presented in this paper are based on the alternated inertial method and the subgradient extragradient method. Weak convergence of the algorithms is established by the adaptive stepsize criterion in Hilbert spaces.},\nkeywords={Alternated inertial method, Pseudomonotone operator,  Variational inequality problem, Subgradient extragradient method},\nabbrev_source_title={J. Nonlinear Convex Anal.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  The goal of this paper is to study some iterative algorithms for solving a pseudomonotone variational inequality in Hilbert spaces. The iterative algorithms presented in this paper are based on the alternated inertial method and the subgradient extragradient method. Weak convergence of the algorithms is established by the adaptive stepsize criterion in Hilbert spaces.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"zhou-tan-li-twoselfadaptiveinertialprojectionalgorithmsforsolvingsplitvariationalinclusionproblems-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Zhou, Z.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Two self-adaptive inertial projection algorithms for solving split variational inclusion problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>AIMS Mathematics</i>, 7(4): 4960–4973.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/ZTL-AIMS2022.pdf\"\n     onclick=\"log_download('zhou-tan-li-twoselfadaptiveinertialprojectionalgorithmsforsolvingsplitvariationalinclusionproblems-2022', 'https://bingtan.me/files/paper/ZTL-AIMS2022.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Two self-adaptive inertial projection algorithms for solving split variational inclusion problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.3934/math.2022276\"\n     onclick=\"log_download('zhou-tan-li-twoselfadaptiveinertialprojectionalgorithmsforsolvingsplitvariationalinclusionproblems-2022', 'http://doi.org/10.3934/math.2022276', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/zhou-tan-li-twoselfadaptiveinertialprojectionalgorithmsforsolvingsplitvariationalinclusionproblems-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('zhou-tan-li-twoselfadaptiveinertialprojectionalgorithmsforsolvingsplitvariationalinclusionproblems-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{ZTL_AIMS22,\nauthor={Zhou, Zheng and Tan, Bing and Li, Songxiao},\ntitle={Two self-adaptive inertial projection algorithms for solving split variational inclusion problems},\njournal={AIMS Mathematics},\nyear={2022},\nvolume={7},\nnumber={4},\npages={4960--4973},\ndoi={10.3934/math.2022276},\nurl={https://bingtan.me/files/paper/ZTL-AIMS2022.pdf},\nabstract={This paper is to analyze the approximation solution of a split variational inclusion problem in the framework of Hilbert spaces. For this purpose, inertial hybrid and shrinking projection algorithms are proposed under the effect of a self-adaptive stepsize which does not require information of the norms of the given operators. The strong convergence properties of the proposed algorithms are obtained under mild constraints. Finally, a numerical experiment is given to illustrate the performance of proposed methods and to compare our algorithms with an existing algorithm.},\nkeywords={Inertial method,  Adaptive stepsize,  Split variational inclusion problem},\nabbrev_source_title={AIMS Math.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This paper is to analyze the approximation solution of a split variational inclusion problem in the framework of Hilbert spaces. For this purpose, inertial hybrid and shrinking projection algorithms are proposed under the effect of a self-adaptive stepsize which does not require information of the norms of the given operators. The strong convergence properties of the proposed algorithms are obtained under mild constraints. Finally, a numerical experiment is given to illustrate the performance of proposed methods and to compare our algorithms with an existing algorithm.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"zhou-tan-li-anacceleratedhybridprojectionmethodwithaselfadaptivestepsizesequenceforsolvingsplitcommonfixedpointproblems-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Zhou, Z.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  An accelerated hybrid projection method with a self-adaptive step-size sequence for solving split common fixed point problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Mathematical Methods in the Applied Sciences</i>, 44(8): 7294–7303.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"><span style=\"color: red\">(<s>ESI Highly Cited Paper</s>)</span></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/ZTL-MMAS2021.pdf\"\n     onclick=\"log_download('zhou-tan-li-anacceleratedhybridprojectionmethodwithaselfadaptivestepsizesequenceforsolvingsplitcommonfixedpointproblems-2021', 'https://bingtan.me/files/paper/ZTL-MMAS2021.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"An accelerated hybrid projection method with a self-adaptive step-size sequence for solving split common fixed point problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1002/mma.7261\"\n     onclick=\"log_download('zhou-tan-li-anacceleratedhybridprojectionmethodwithaselfadaptivestepsizesequenceforsolvingsplitcommonfixedpointproblems-2021', 'http://doi.org/10.1002/mma.7261', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/zhou-tan-li-anacceleratedhybridprojectionmethodwithaselfadaptivestepsizesequenceforsolvingsplitcommonfixedpointproblems-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('zhou-tan-li-anacceleratedhybridprojectionmethodwithaselfadaptivestepsizesequenceforsolvingsplitcommonfixedpointproblems-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{ZTL_MMAS21,\nauthor={Zhou, Zheng and Tan, Bing and Li, Songxiao},\ntitle={An accelerated hybrid projection method with a self-adaptive step-size sequence for solving split common fixed point problems},\njournal={Mathematical Methods in the Applied Sciences},\nyear={2021},\nvolume={44},\nnumber={8},\npages={7294--7303},\ndoi={10.1002/mma.7261},\nurl={https://bingtan.me/files/paper/ZTL-MMAS2021.pdf},\nabstract={This paper attempts to solve the split common fixed point problem for demicontractive mappings. We give an accelerated hybrid projection algorithm that combines the hybrid projection method and the inertial technique. The strong convergence theorem of this algorithm is obtained under mild conditions by a self-adaptive step-size sequence, which does not need prior knowledge of the operator norm. Some numerical experiments in infinite-dimensional Hilbert spaces are provided to illustrate the reliability and robustness of the algorithm and also to compare it with existing ones.},\nkeywords={Demicontractive mapping,  Hybrid projection method,  Inertial method,  Split common fixed point problem},\nabbrev_source_title={Math. Methods Appl. Sci.},\nbibbase_note={&lt;span style=&quot;color: red&quot;&gt;(&lt;s&gt;ESI Highly Cited Paper&lt;/s&gt;)&lt;/span&gt;},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This paper attempts to solve the split common fixed point problem for demicontractive mappings. We give an accelerated hybrid projection algorithm that combines the hybrid projection method and the inertial technique. The strong convergence theorem of this algorithm is obtained under mild conditions by a self-adaptive step-size sequence, which does not need prior knowledge of the operator norm. Some numerical experiments in infinite-dimensional Hilbert spaces are provided to illustrate the reliability and robustness of the algorithm and also to compare it with existing ones.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-zhou-qin-acceleratedprojectionbasedforwardbackwardsplittingalgorithmsformonotoneinclusionproblems-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Zhou, Z.;  and Qin, X.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Accelerated projection-based forward-backward splitting algorithms for monotone inclusion problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Applied Analysis and Computation</i>, 10(5): 2184–2197.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TZQ-JAAC2020.pdf\"\n     onclick=\"log_download('tan-zhou-qin-acceleratedprojectionbasedforwardbackwardsplittingalgorithmsformonotoneinclusionproblems-2020', 'https://bingtan.me/files/paper/TZQ-JAAC2020.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Accelerated projection-based forward-backward splitting algorithms for monotone inclusion problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.11948/20190363\"\n     onclick=\"log_download('tan-zhou-qin-acceleratedprojectionbasedforwardbackwardsplittingalgorithmsformonotoneinclusionproblems-2020', 'http://doi.org/10.11948/20190363', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-zhou-qin-acceleratedprojectionbasedforwardbackwardsplittingalgorithmsformonotoneinclusionproblems-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-zhou-qin-acceleratedprojectionbasedforwardbackwardsplittingalgorithmsformonotoneinclusionproblems-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TZQ_JAAC20,\nauthor={Tan, Bing and Zhou, Zheng and Qin, Xiaolong},\ntitle={Accelerated projection-based forward-backward splitting algorithms for monotone inclusion problems},\njournal={Journal of Applied Analysis and Computation},\nyear={2020},\nvolume={10},\nnumber={5},\npages={2184--2197},\ndoi={10.11948/20190363},\nurl={https://bingtan.me/files/paper/TZQ-JAAC2020.pdf},\nabstract={In this paper, based on inertial and Tseng&#x27;s ideas, we propose two projection-based algorithms to solve a monotone inclusion problem in infinite dimensional Hilbert spaces. Solution theorems of strong convergence are obtained under the certain conditions. Some numerical experiments are presented to illustrate that our algorithms are efficient than the existing results.},\nkeywords={Forward-backward splitting algorithm,  Inclusion problem,  Monotone operator,  Strong convergence},\nabbrev_source_title={J. Appl. Anal. Comput.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, based on inertial and Tseng's ideas, we propose two projection-based algorithms to solve a monotone inclusion problem in infinite dimensional Hilbert spaces. Solution theorems of strong convergence are obtained under the certain conditions. Some numerical experiments are presented to illustrate that our algorithms are efficient than the existing results.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"tan-zhou-li-strongconvergenceofmodifiedinertialmannalgorithmsfornonexpansivemappings-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>; Zhou, Z.;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  Strong convergence of modified inertial mann algorithms for nonexpansive mappings.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Mathematics</i>, 8(4): 462.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/TZL-Math2020.pdf\"\n     onclick=\"log_download('tan-zhou-li-strongconvergenceofmodifiedinertialmannalgorithmsfornonexpansivemappings-2020', 'https://bingtan.me/files/paper/TZL-Math2020.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Strong convergence of modified inertial mann algorithms for nonexpansive mappings [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.3390/math8040462\"\n     onclick=\"log_download('tan-zhou-li-strongconvergenceofmodifiedinertialmannalgorithmsfornonexpansivemappings-2020', 'http://doi.org/10.3390/math8040462', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/tan-zhou-li-strongconvergenceofmodifiedinertialmannalgorithmsfornonexpansivemappings-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('tan-zhou-li-strongconvergenceofmodifiedinertialmannalgorithmsfornonexpansivemappings-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{TZL_MATH20,\nauthor={Tan, Bing and Zhou, Zheng and Li, Songxiao},\ntitle={Strong convergence of modified inertial mann algorithms for nonexpansive mappings},\njournal={Mathematics},\nyear={2020},\nvolume={8},\nnumber={4},\ndoi={10.3390/math8040462},\npages={462},\nurl={https://bingtan.me/files/paper/TZL-Math2020.pdf},\nabstract={We investigated two new modified inertial Mann Halpern and inertial Mann viscosity algorithms for solving fixed point problems. Strong convergence theorems under some fewer restricted conditions are established in the framework of infinite dimensional Hilbert spaces. Finally, some numerical examples are provided to support our main results. The algorithms and results presented in this paper can generalize and extend corresponding results previously known in the literature.},\nkeywords={Halpern method,  Inertial method,  Nonexpansive mapping,  Strong convergence,  Viscosity method},\nabbrev_source_title={Mathematics},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We investigated two new modified inertial Mann Halpern and inertial Mann viscosity algorithms for solving fixed point problems. Strong convergence theorems under some fewer restricted conditions are established in the framework of infinite dimensional Hilbert spaces. Finally, some numerical examples are provided to support our main results. The algorithms and results presented in this paper can generalize and extend corresponding results previously known in the literature.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"zhou-tan-li-anewacceleratedselfadaptivestepsizealgorithmwithexcellentstabilityforsplitcommonfixedpointproblems-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Zhou, Z.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  A new accelerated self-adaptive stepsize algorithm with excellent stability for split common fixed point problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Computational and Applied Mathematics</i>, 39(3): 220.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/ZTL-COAM2020.pdf\"\n     onclick=\"log_download('zhou-tan-li-anewacceleratedselfadaptivestepsizealgorithmwithexcellentstabilityforsplitcommonfixedpointproblems-2020', 'https://bingtan.me/files/paper/ZTL-COAM2020.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"A new accelerated self-adaptive stepsize algorithm with excellent stability for split common fixed point problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s40314-020-01237-0\"\n     onclick=\"log_download('zhou-tan-li-anewacceleratedselfadaptivestepsizealgorithmwithexcellentstabilityforsplitcommonfixedpointproblems-2020', 'http://doi.org/10.1007/s40314-020-01237-0', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/zhou-tan-li-anewacceleratedselfadaptivestepsizealgorithmwithexcellentstabilityforsplitcommonfixedpointproblems-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('zhou-tan-li-anewacceleratedselfadaptivestepsizealgorithmwithexcellentstabilityforsplitcommonfixedpointproblems-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{ZTL_COAM20,\nauthor={Zhou, Zheng and Tan, Bing and Li, Songxiao},\ntitle={A new accelerated self-adaptive stepsize algorithm with excellent stability for split common fixed point problems},\njournal={Computational and Applied Mathematics},\nyear={2020},\nvolume={39},\nnumber={3},\ndoi={10.1007/s40314-020-01237-0},\npages={220},\nurl={https://bingtan.me/files/paper/ZTL-COAM2020.pdf},\nabstract={In the framework of Hilbert spaces, we study the solutions of split common fixed point problems. A new accelerated self-adaptive stepsize algorithm with excellent stability is proposed under the effects of inertial techniques and Meir–Keeler contraction mappings. The strong convergence theorems are obtained without prior knowledge of operator norms. Finally, in applications, our main results in this paper are applied to signal recovery problems.},\nkeywords={Inertial method,  Meir–Keeler contraction,  Adaptive stepsize,  Signal processing problem, Split common fixed point problem},\nabbrev_source_title={Comput. Appl. Math.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In the framework of Hilbert spaces, we study the solutions of split common fixed point problems. A new accelerated self-adaptive stepsize algorithm with excellent stability is proposed under the effects of inertial techniques and Meir–Keeler contraction mappings. The strong convergence theorems are obtained without prior knowledge of operator norms. Finally, in applications, our main results in this paper are applied to signal recovery problems.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"zhou-tan-li-aninertialshrinkingprojectionalgorithmforsplitcommonfixedpointproblems-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Zhou, Z.; <a class=\"bibbase author link\" href=\"https://bingtan.me/pubs_author.html\">Tan, B.</a>;  and Li, S.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  An inertial shrinking projection algorithm for split common fixed point problems.\n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Applied Analysis and Computation</i>, 10(5): 2104–2120.  2020.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://bingtan.me/files/paper/ZTL-JAAC2020.pdf\"\n     onclick=\"log_download('zhou-tan-li-aninertialshrinkingprojectionalgorithmforsplitcommonfixedpointproblems-2020', 'https://bingtan.me/files/paper/ZTL-JAAC2020.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"An inertial shrinking projection algorithm for split common fixed point problems [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.11948/20190330\"\n     onclick=\"log_download('zhou-tan-li-aninertialshrinkingprojectionalgorithmforsplitcommonfixedpointproblems-2020', 'http://doi.org/10.11948/20190330', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/zhou-tan-li-aninertialshrinkingprojectionalgorithmforsplitcommonfixedpointproblems-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('zhou-tan-li-aninertialshrinkingprojectionalgorithmforsplitcommonfixedpointproblems-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@ARTICLE{ZTL_JAAC20,\nauthor={Zhou, Zheng and Tan, Bing and Li, Songxiao},\ntitle={An inertial shrinking projection algorithm for split common fixed point problems},\njournal={Journal of Applied Analysis and Computation},\nyear={2020},\nvolume={10},\nnumber={5},\npages={2104--2120},\ndoi={10.11948/20190330},\nurl={https://bingtan.me/files/paper/ZTL-JAAC2020.pdf},\nabstract={In this paper, the purpose is to introduce and study a new modified shrinking projection algorithm with inertial effects, which solves split common fixed point problems in Banach spaces. The corresponding strong convergence theorems are obtained without the assumption of semi-compactness on map-pings. Finally, some numerical examples are presented to illustrate the results in this paper.},\nkeywords={Inertial method,  Shrinking projection method,  Split common fixed point problem,  Strong convergence},\nabbrev_source_title={J. Appl. Anal. Comput.},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, the purpose is to introduce and study a new modified shrinking projection algorithm with inertial effects, which solves split common fixed point problems in Banach spaces. The corresponding strong convergence theorems are obtained without the assumption of semi-compactness on map-pings. Finally, some numerical examples are presented to illustrate the results in this paper.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n\n\n\n  </div>\n\n\n  <!-- Modal -->\n\n  <!-- <iframe id=\"bibbase_network_frame\" -->\n  <!--         src=\"//bibbase.org/network/control\" -->\n  <!--         style=\"display: none;\"> -->\n  <!-- </iframe> -->\n\n</div>\n"}; document.write(bibbase_data.data);