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{Shuoran Li and Pengcheng Xie and Zihao Zhou and others},\\n  title     = {Simulation of Interaction of Folded Waveguide Space Traveling Wave Tubes with Derivative-Free Mixed-Integer-Based {NEWUOA} Algorithm},\\n  booktitle = {2021 7th International Conference on Computer and Communications (ICCC)},\\n  year      = {2021},\\n  pages     = {1215--1219},\\n  doi       = {10.1109/ICCC54389.2021.9674410},\\n  url       = {https://doi.org/10.1109/ICCC54389.2021.9674410},\\n  keywords  = {optimization}\\n}\\n\",\"author_short\":[\"Li, S.\",\"Xie, P.\",\"Zhou, Z.\",\"others\"],\"key\":\"li-xie-zhou-etal-2021-newuoa\",\"id\":\"li-xie-zhou-etal-2021-newuoa\",\"bibbaseid\":\"li-xie-zhou-others-simulationofinteractionoffoldedwaveguidespacetravelingwavetubeswithderivativefreemixedintegerbasednewuoaalgorithm-2021\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://doi.org/10.1109/ICCC54389.2021.9674410\"},\"keyword\":[\"optimization\"],\"metadata\":{\"authorlinks\":{\"xie, 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download=\"xpcpublication.bib\" href=\"data:text/bibtex;base64,@article{xie-wild-2026-remu,
  author  = {Pengcheng Xie and Stefan M. Wild},
  title   = {{ReMU}: Regional Minimal Updating for Model-Based Derivative-Free Optimization},
  journal = {Optimization Methods and Software},
  year    = {2026},
  pages   = {1--30},
  doi     = {10.1080/10556788.2026.2660368},
  url     = {https://doi.org/10.1080/10556788.2026.2660368},
  keywords = {optimization}
}



@article{xie-yuan-2025-improved-underdetermined-model,
  author  = {Pengcheng Xie and Ya-xiang Yuan},
  title   = {A New Derivative-Free Method Using an Improved Underdetermined Quadratic Interpolation Model},
  journal = {SIAM Journal on Optimization},
  year    = {2025},
  volume  = {35},
  number  = {2},
  pages   = {1110--1133},
  doi     = {10.1137/23M1582023},
  url     = {https://doi.org/10.1137/23M1582023},
  keywords = {optimization}
}



@article{xie-yuan-2026-h2-updating,
  author  = {Pengcheng Xie and Ya-xiang Yuan},
  title   = {Least {$H^2$} Norm Updating of Quadratic Interpolation Models for Derivative-Free Trust-Region Algorithms},
  journal = {IMA Journal of Numerical Analysis},
  year    = {2026},
  volume  = {46},
  number  = {1},
  pages   = {21--50},
  doi     = {10.1093/imanum/drae106},
  url     = {https://doi.org/10.1093/imanum/drae106},
  keywords = {optimization}
}



@article{xie-2025-distance-reduction,
  author  = {Pengcheng Xie},
  title   = {Sufficient Conditions for Error Distance Reduction in the {$\ell_2$}-Norm Trust Region Between Minimizers of Local Nonconvex Multivariate Quadratic Approximates},
  journal = {Journal of Computational and Applied Mathematics},
  year    = {2025},
  volume  = {453},
  pages   = {116146},
  doi     = {10.1016/j.cam.2024.116146},
  url     = {https://doi.org/10.1016/j.cam.2024.116146},
  keywords = {optimization}
}



@article{xie-yuan-2026-2d-mosub,
  author  = {Pengcheng Xie and Ya-xiang Yuan},
  title   = {A New Two-Dimensional Model-Based Subspace Method for Large-Scale Unconstrained Derivative-Free Optimization: {2D-MoSub}},
  journal = {Optimization Methods and Software},
  year    = {2026},
  volume  = {41},
  number  = {1},
  pages   = {118--150},
  doi     = {10.1080/10556788.2025.2601670},
  url     = {https://doi.org/10.1080/10556788.2025.2601670},
  keywords = {optimization}
}



@article{xie-yuan-2025-dfoto,
  author  = {Pengcheng Xie and Ya-xiang Yuan},
  title   = {Derivative-Free Optimization with Transformed Objective Functions ({DFOTO}) and the Algorithm Based on the Least {Frobenius} Norm Updating Quadratic Model},
  journal = {Journal of the Operations Research Society of China},
  year    = {2025},
  volume  = {13},
  pages   = {327--363},
  doi     = {10.1007/s40305-023-00532-x},
  url     = {https://doi.org/10.1007/s40305-023-00532-x},
  keywords = {optimization}
}



@article{li-zhou-xie-li-2025-spectral-lm-deflation,
  author  = {Lin Li and Yuheng Zhou and Pengcheng Xie and Huiyuan Li},
  title   = {A Spectral {Levenberg--Marquardt}-Deflation Method for Multiple Solutions of Semilinear Elliptic Systems},
  journal = {Journal of Computational and Applied Mathematics},
  year    = {2025},
  volume  = {475},
  pages   = {116998},
  doi     = {10.1016/j.cam.2025.116998},
  url     = {https://doi.org/10.1016/j.cam.2025.116998},
  keywords = {numerical PDE}
}



@article{ye-li-xie-yu-2025-adaptive-deflation,
  author  = {Yangyi Ye and Lin Li and Pengcheng Xie and Haijun Yu},
  title   = {An Improved Adaptive Orthogonal Basis Deflation Method for Multiple Solutions with Applications to Nonlinear Elliptic Equations in Varying Domains},
  journal = {Journal of Computational Mathematics},
  year    = {2025},
  volume  = {44},
  number  = {3},
  pages   = {794--818},
  doi     = {10.4208/jcm.2505-m2024-0276},
  url     = {https://doi.org/10.4208/jcm.2505-m2024-0276},
  keywords = {numerical PDE}
}



@article{xie-yuan-2023-line-search-trust-region,
  author  = {Pengcheng Xie and Ya-xiang Yuan},
  title   = {A Derivative-Free Optimization Algorithm Combining Line-Search and Trust-Region Techniques},
  journal = {Chinese Annals of Mathematics, Series B},
  year    = {2023},
  volume  = {44},
  number  = {5},
  pages   = {693--708},
  doi     = {10.1007/s11401-023-0040-y},
  url     = {https://doi.org/10.1007/s11401-023-0040-y},
  keywords = {optimization}
}



@article{xie-2024-multidam,
  author  = {Pengcheng Xie},
  title   = {The Modeling and Optimization of a Multi-Dam System},
  journal = {Applied and Computational Mathematics},
  year    = {2024},
  volume  = {13},
  number  = {5},
  pages   = {140--152},
  doi     = {10.11648/j.acm.20241305.13},
  url     = {https://doi.org/10.11648/j.acm.20241305.13},
  keywords = {optimization}
}



@article{xie-2023-ellipsoid,
  author  = {Pengcheng Xie},
  title   = {A Derivative-Free Trust-Region Method for Optimization on the Ellipsoid},
  journal = {Journal of Physics: Conference Series},
  year    = {2023},
  volume  = {2620},
  pages   = {012007},
  doi     = {10.1088/1742-6596/2620/1/012007},
  url     = {https://doi.org/10.1088/1742-6596/2620/1/012007},
  note    = {Presented at the 2023 International Conference on Advances in Computer Science and Engineering Technology},
  keywords = {optimization}
}



@inproceedings{xie-tao-2019-acc,
  author    = {Pengcheng Xie and Molei Tao},
  title     = {Parametric Resonant Control of Macroscopic Behaviors of Multiple Oscillators},
  booktitle = {2019 American Control Conference (ACC)},
  year      = {2019},
  pages     = {1898--1905},
  doi       = {10.23919/ACC.2019.8814709},
  url       = {https://doi.org/10.23919/ACC.2019.8814709},
  keywords  = {control}
}



@article{dzahini-wild-xie-2025-inverse-problems,
  author  = {Kwassi J. Dzahini and Stefan M. Wild and Pengcheng Xie},
  title   = {Optimization Approaches for Solving Inverse Problems Under Uncertainty},
  journal = {Inverse Methods for Complex Systems under Uncertainty Workshop},
  year    = {2025},
  note    = {Position paper, U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research},
  url     = {https://www.orau.gov/support_files/2025InverseMethods/WildS.pdf},
  keywords = {optimization}
}



@misc{huang-li-xie-2026-h1-time-fractional,
  author        = {Liangcai Huang and Lin Li and Pengcheng Xie},
  title         = {Second-order {$H^1$}-norm Error Analysis for Time-Fractional Advection-Dispersion Equations Based on the Fast Averaged {L1} Method},
  year          = {2026},
  eprint        = {2606.22083},
  archivePrefix = {arXiv},
  primaryClass  = {math.NA},
  url           = {https://arxiv.org/abs/2606.22083},
  keywords      = {numerical PDE}
}



@misc{hu-xie-yuan-zhang-2026-matro,
  author        = {Wei Hu and Pengcheng Xie and Ya-xiang Yuan and Li Zhang},
  title         = {{MATRO}: Metric-Aware Fully Quadratic Trust Regions for Derivative-Free Optimization},
  year          = {2026},
  eprint        = {2605.30845},
  archivePrefix = {arXiv},
  primaryClass  = {math.OC},
  url           = {https://arxiv.org/abs/2605.30845},
  keywords      = {optimization}
}



@misc{hu-xie-yuan-zhang-2026-bup-tr,
  author        = {Wei Hu and Pengcheng Xie and Ya-xiang Yuan and Li Zhang},
  title         = {{BUP-TR}: {Bayesian} Underdetermined Projection Trust-Region Methods for Derivative-Free Optimization},
  year          = {2026},
  eprint        = {2605.30841},
  archivePrefix = {arXiv},
  primaryClass  = {math.OC},
  url           = {https://arxiv.org/abs/2605.30841},
  keywords      = {optimization}
}



@misc{hu-xie-yuan-zhang-2026-distributed-newton,
  author        = {Wei Hu and Pengcheng Xie and Ya-xiang Yuan and Li Zhang},
  title         = {Distributed Gradient-Regularized {Newton} Method: Scheduled Consensus and {$O(\epsilon^{-1})$} Global Iteration Complexity},
  year          = {2026},
  eprint        = {2605.19396},
  archivePrefix = {arXiv},
  primaryClass  = {math.OC},
  url           = {https://arxiv.org/abs/2605.19396},
  keywords      = {optimization}
}



@misc{xie-2026-pbbo,
  author        = {Pengcheng Xie},
  title         = {Privacy-Preserving Black-Box Optimization ({PBBO}): Theory and the Model-Based Algorithm {DFOp}},
  year          = {2026},
  eprint        = {2601.11570},
  archivePrefix = {arXiv},
  primaryClass  = {cs.CR},
  url           = {https://arxiv.org/abs/2601.11570},
  keywords      = {optimization, privacy}
}



@misc{li-xie-zhang-2025-novel-numerical-method,
  author        = {Lin Li and Pengcheng Xie and Li Zhang},
  title         = {A Novel Numerical Method Tailored for Unconstrained Optimization Problems},
  year          = {2025},
  eprint        = {2504.02832},
  archivePrefix = {arXiv},
  primaryClass  = {math.OC},
  url           = {https://arxiv.org/abs/2504.02832},
  keywords      = {optimization}
}



@misc{xie-zhou-zhou-2025-shape-based-optimization,
  author        = {Pengcheng Xie and Zihao Zhou and Zijian Zhou},
  title         = {Objective Value Change and Shape-Based Accelerated Optimization for Neural Network Approximation},
  year          = {2025},
  eprint        = {2508.20290},
  archivePrefix = {arXiv},
  primaryClass  = {cs.LG},
  url           = {https://arxiv.org/abs/2508.20290},
  keywords      = {machine learning, optimization}
}



@misc{he-xie-2025-model-driven-subspaces,
  author        = {Yitong He and Pengcheng Xie},
  title         = {Model-Driven Subspaces for Large-Scale Optimization with Local Approximation Strategy},
  year          = {2025},
  eprint        = {2509.08256},
  archivePrefix = {arXiv},
  primaryClass  = {math.OC},
  url           = {https://arxiv.org/abs/2509.08256},
  keywords      = {optimization}
}



@misc{xie-2024-lambda-poisedness-lof,
  author        = {Pengcheng Xie},
  title         = {On the Relationship Between {$\Lambda$}-Poisedness in Derivative-Free Optimization and Outliers in Local Outlier Factor},
  year          = {2024},
  eprint        = {2407.17529},
  archivePrefix = {arXiv},
  primaryClass  = {math.OC},
  url           = {https://arxiv.org/abs/2407.17529},
  keywords      = {optimization, approximation}
}



@misc{xie-wild-2024-h2-barycenter,
  author   = {Pengcheng Xie and Stefan M. Wild},
  title    = {Barycenter of the Weight-Coefficient Region of Least-Weighted {$H^2$} Norm Updating Quadratic Models with Vanishing Trust-Region Radius},
  year     = {2024},
  note     = {SIAM Northern and Central California Sectional Conference (NCC24), Early Career Travel Award},
  keywords = {optimization}
}



@misc{xie-etal-2024-l-change,
  author   = {Pengcheng Xie and others},
  title    = {A Novel Local Analysis of Objectives Approximated by Neural Networks: {L-Change}},
  year     = {2024},
  note     = {International Conference on Mathematical Theory of Deep Learning (MTDL)},
  keywords = {machine learning, neural network}
}



@misc{hu-xie-zhang-yuan-2024-lc3rqn,
  author   = {Wei Hu and Pengcheng Xie and Li Zhang and Ya-xiang Yuan},
  title    = {A Low-Computation-Cost Cubic-Regularized Quasi-{Newton} Method for Distributed Optimization: {LC3RQN}},
  year     = {2024},
  url      = {https://lsec.cc.ac.cn/~moa2024/Poster_List.pdf},
  keywords = {optimization}
}



@misc{xie-2024-multiple-solutions,
  author   = {Pengcheng Xie},
  title    = {An Efficient Derivative-Free Method for Finding Multiple Solutions},
  year     = {2024},
  note     = {Manuscript},
  keywords = {numerical PDE}
}



@misc{xie-2024-invariant-distribution,
  author   = {Pengcheng Xie},
  title    = {A Note on the Invariant Distribution of a Stochastic Dynamical System},
  year     = {2024},
  doi      = {10.12074/202304.01048},
  url      = {https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4910398},
  keywords = {control}
}



@inproceedings{li-xie-zhou-etal-2021-newuoa,
  author    = {Shuoran Li and Pengcheng Xie and Zihao Zhou and others},
  title     = {Simulation of Interaction of Folded Waveguide Space Traveling Wave Tubes with Derivative-Free Mixed-Integer-Based {NEWUOA} Algorithm},
  booktitle = {2021 7th International Conference on Computer and Communications (ICCC)},
  year      = {2021},
  pages     = {1215--1219},
  doi       = {10.1109/ICCC54389.2021.9674410},
  url       = {https://doi.org/10.1109/ICCC54389.2021.9674410},
  keywords  = {optimization}
}
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In order to keep using Mendeley with BibBase past April\n        14th, you need to:\n        <ol>\n          <li>renew the authorization for BibBase on Mendeley, and</li>\n          <li>update the BibBase URL\n            in your page the same way you did when you initially set up\n            this page.\n          </li>\n        </ol>\n      </p>\n\n      <p>\n        <a href=\"http://bibbase.org/cgi-bin/mendeley2/get.py\">\n          <i class=\"fa fa-angle-double-right\"></i>\n          Fix it now</a>\n      </p>\n    </div>\n\n  </div>\n\n\n  <div id=\"bibbase_body\">\n    \n  \n  <div class=\"bibbase_group_whole\" id=\"group_2026\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2026')\"\n      onkeypress=\"toggleGroup('group_2026')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2026</span>\n      <span class=\"bibbase_group_count\">\n        \n        (8)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"xie-wild-remuregionalminimalupdatingformodelbasedderivativefreeoptimization-2026\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://doi.org/10.1080/10556788.2026.2660368\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'xie-wild-remuregionalminimalupdatingformodelbasedderivativefreeoptimization-2026', 'https://doi.org/10.1080/10556788.2026.2660368', event);\">\n    ReMU: Regional Minimal Updating for Model-Based Derivative-Free Optimization.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://pxie98.github.io/publication.html\">Xie, P.</a>;  and Wild, S. M.\n</span>\n\n  \n\n</span>\n\n  <i>Optimization Methods and Software</i>,1–30.  2026.\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://doi.org/10.1080/10556788.2026.2660368\"\n     onclick=\"log_download('xie-wild-remuregionalminimalupdatingformodelbasedderivativefreeoptimization-2026', 'https://doi.org/10.1080/10556788.2026.2660368', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"ReMU: Regional Minimal Updating for Model-Based Derivative-Free Optimization [link]\"\n       title=\"Paper\"\n       style=\"max-height: 1em;\"\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/10.1080/10556788.2026.2660368\"\n     onclick=\"log_download('xie-wild-remuregionalminimalupdatingformodelbasedderivativefreeoptimization-2026', 'http://doi.org/10.1080/10556788.2026.2660368', 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-wild-remuregionalminimalupdatingformodelbasedderivativefreeoptimization-2026\"\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\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('xie-wild-remuregionalminimalupdatingformodelbasedderivativefreeoptimization-2026')\" -->\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</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{xie-wild-2026-remu,\n  author  = {Pengcheng Xie and Stefan M. Wild},\n  title   = {{ReMU}: Regional Minimal Updating for Model-Based Derivative-Free Optimization},\n  journal = {Optimization Methods and Software},\n  year    = {2026},\n  pages   = {1--30},\n  doi     = {10.1080/10556788.2026.2660368},\n  url     = {https://doi.org/10.1080/10556788.2026.2660368},\n  keywords = {optimization}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"xie-yuan-leasth2normupdatingofquadraticinterpolationmodelsforderivativefreetrustregionalgorithms-2026\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://doi.org/10.1093/imanum/drae106\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'xie-yuan-leasth2normupdatingofquadraticinterpolationmodelsforderivativefreetrustregionalgorithms-2026', 'https://doi.org/10.1093/imanum/drae106', event);\">\n    Least $H^2$ Norm Updating of Quadratic Interpolation Models for Derivative-Free Trust-Region Algorithms.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://pxie98.github.io/publication.html\">Xie, P.</a>;  and Yuan, Y.\n</span>\n\n  \n\n</span>\n\n  <i>IMA Journal of Numerical Analysis</i>, 46(1): 21–50.  2026.\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://doi.org/10.1093/imanum/drae106\"\n     onclick=\"log_download('xie-yuan-leasth2normupdatingofquadraticinterpolationmodelsforderivativefreetrustregionalgorithms-2026', 'https://doi.org/10.1093/imanum/drae106', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Least $H^2$ Norm Updating of Quadratic Interpolation Models for Derivative-Free Trust-Region Algorithms [link]\"\n       title=\"Paper\"\n       style=\"max-height: 1em;\"\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/10.1093/imanum/drae106\"\n     onclick=\"log_download('xie-yuan-leasth2normupdatingofquadraticinterpolationmodelsforderivativefreetrustregionalgorithms-2026', 'http://doi.org/10.1093/imanum/drae106', 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-yuan-leasth2normupdatingofquadraticinterpolationmodelsforderivativefreetrustregionalgorithms-2026\"\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\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('xie-yuan-leasth2normupdatingofquadraticinterpolationmodelsforderivativefreetrustregionalgorithms-2026')\" -->\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</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{xie-yuan-2026-h2-updating,\n  author  = {Pengcheng Xie and Ya-xiang Yuan},\n  title   = {Least {$H^2$} Norm Updating of Quadratic Interpolation Models for Derivative-Free Trust-Region Algorithms},\n  journal = {IMA Journal of Numerical Analysis},\n  year    = {2026},\n  volume  = {46},\n  number  = {1},\n  pages   = {21--50},\n  doi     = {10.1093/imanum/drae106},\n  url     = {https://doi.org/10.1093/imanum/drae106},\n  keywords = {optimization}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"xie-yuan-anewtwodimensionalmodelbasedsubspacemethodforlargescaleunconstrainedderivativefreeoptimization2dmosub-2026\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://doi.org/10.1080/10556788.2025.2601670\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'xie-yuan-anewtwodimensionalmodelbasedsubspacemethodforlargescaleunconstrainedderivativefreeoptimization2dmosub-2026', 'https://doi.org/10.1080/10556788.2025.2601670', event);\">\n    A New Two-Dimensional Model-Based Subspace Method for Large-Scale Unconstrained Derivative-Free Optimization: 2D-MoSub.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://pxie98.github.io/publication.html\">Xie, P.</a>;  and Yuan, Y.\n</span>\n\n  \n\n</span>\n\n  <i>Optimization Methods and Software</i>, 41(1): 118–150.  2026.\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://doi.org/10.1080/10556788.2025.2601670\"\n     onclick=\"log_download('xie-yuan-anewtwodimensionalmodelbasedsubspacemethodforlargescaleunconstrainedderivativefreeoptimization2dmosub-2026', 'https://doi.org/10.1080/10556788.2025.2601670', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"A New Two-Dimensional Model-Based Subspace Method for Large-Scale Unconstrained Derivative-Free Optimization: 2D-MoSub [link]\"\n       title=\"Paper\"\n       style=\"max-height: 1em;\"\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/10.1080/10556788.2025.2601670\"\n     onclick=\"log_download('xie-yuan-anewtwodimensionalmodelbasedsubspacemethodforlargescaleunconstrainedderivativefreeoptimization2dmosub-2026', 'http://doi.org/10.1080/10556788.2025.2601670', 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-yuan-anewtwodimensionalmodelbasedsubspacemethodforlargescaleunconstrainedderivativefreeoptimization2dmosub-2026\"\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\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('xie-yuan-anewtwodimensionalmodelbasedsubspacemethodforlargescaleunconstrainedderivativefreeoptimization2dmosub-2026')\" -->\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</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{xie-yuan-2026-2d-mosub,\n  author  = {Pengcheng Xie and Ya-xiang Yuan},\n  title   = {A New Two-Dimensional Model-Based Subspace Method for Large-Scale Unconstrained Derivative-Free Optimization: {2D-MoSub}},\n  journal = {Optimization Methods and Software},\n  year    = {2026},\n  volume  = {41},\n  number  = {1},\n  pages   = {118--150},\n  doi     = {10.1080/10556788.2025.2601670},\n  url     = {https://doi.org/10.1080/10556788.2025.2601670},\n  keywords = {optimization}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"huang-li-xie-secondorderh1normerroranalysisfortimefractionaladvectiondispersionequationsbasedonthefastaveragedl1method-2026\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://arxiv.org/abs/2606.22083\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'huang-li-xie-secondorderh1normerroranalysisfortimefractionaladvectiondispersionequationsbasedonthefastaveragedl1method-2026', 'https://arxiv.org/abs/2606.22083', event);\">\n    Second-order $H^1$-norm Error Analysis for Time-Fractional Advection-Dispersion Equations Based on the Fast Averaged L1 Method.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Huang, L.; Li, L.;  and <a class=\"bibbase author link\" href=\"https://pxie98.github.io/publication.html\">Xie, P.</a>\n</span>\n\n  \n\n</span>\n\n   2026.\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://arxiv.org/abs/2606.22083\"\n     onclick=\"log_download('huang-li-xie-secondorderh1normerroranalysisfortimefractionaladvectiondispersionequationsbasedonthefastaveragedl1method-2026', 'https://arxiv.org/abs/2606.22083', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Second-order $H^1$-norm Error Analysis for Time-Fractional Advection-Dispersion Equations Based on the Fast Averaged L1 Method [link]\"\n       title=\"Paper\"\n       style=\"max-height: 1em;\"\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/huang-li-xie-secondorderh1normerroranalysisfortimefractionaladvectiondispersionequationsbasedonthefastaveragedl1method-2026\"\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\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('huang-li-xie-secondorderh1normerroranalysisfortimefractionaladvectiondispersionequationsbasedonthefastaveragedl1method-2026')\" -->\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</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@misc{huang-li-xie-2026-h1-time-fractional,\n  author        = {Liangcai Huang and Lin Li and Pengcheng Xie},\n  title         = {Second-order {$H^1$}-norm Error Analysis for Time-Fractional Advection-Dispersion Equations Based on the Fast Averaged {L1} Method},\n  year          = {2026},\n  eprint        = {2606.22083},\n  archivePrefix = {arXiv},\n  primaryClass  = {math.NA},\n  url           = {https://arxiv.org/abs/2606.22083},\n  keywords      = {numerical PDE}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"hu-xie-yuan-zhang-matrometricawarefullyquadratictrustregionsforderivativefreeoptimization-2026\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://arxiv.org/abs/2605.30845\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'hu-xie-yuan-zhang-matrometricawarefullyquadratictrustregionsforderivativefreeoptimization-2026', 'https://arxiv.org/abs/2605.30845', event);\">\n    MATRO: Metric-Aware Fully Quadratic Trust Regions for Derivative-Free Optimization.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Hu, W.; <a class=\"bibbase author link\" href=\"https://pxie98.github.io/publication.html\">Xie, P.</a>; Yuan, Y.;  and Zhang, L.\n</span>\n\n  \n\n</span>\n\n   2026.\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://arxiv.org/abs/2605.30845\"\n     onclick=\"log_download('hu-xie-yuan-zhang-matrometricawarefullyquadratictrustregionsforderivativefreeoptimization-2026', 'https://arxiv.org/abs/2605.30845', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"MATRO: Metric-Aware Fully Quadratic Trust Regions for Derivative-Free Optimization [link]\"\n       title=\"Paper\"\n       style=\"max-height: 1em;\"\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/hu-xie-yuan-zhang-matrometricawarefullyquadratictrustregionsforderivativefreeoptimization-2026\"\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\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('hu-xie-yuan-zhang-matrometricawarefullyquadratictrustregionsforderivativefreeoptimization-2026')\" -->\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</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@misc{hu-xie-yuan-zhang-2026-matro,\n  author        = {Wei Hu and Pengcheng Xie and Ya-xiang Yuan and Li Zhang},\n  title         = {{MATRO}: Metric-Aware Fully Quadratic Trust Regions for Derivative-Free Optimization},\n  year          = {2026},\n  eprint        = {2605.30845},\n  archivePrefix = {arXiv},\n  primaryClass  = {math.OC},\n  url           = {https://arxiv.org/abs/2605.30845},\n  keywords      = {optimization}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"hu-xie-yuan-zhang-buptrbayesianunderdeterminedprojectiontrustregionmethodsforderivativefreeoptimization-2026\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://arxiv.org/abs/2605.30841\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'hu-xie-yuan-zhang-buptrbayesianunderdeterminedprojectiontrustregionmethodsforderivativefreeoptimization-2026', 'https://arxiv.org/abs/2605.30841', event);\">\n    BUP-TR: Bayesian Underdetermined Projection Trust-Region Methods for Derivative-Free Optimization.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Hu, W.; <a class=\"bibbase author link\" href=\"https://pxie98.github.io/publication.html\">Xie, P.</a>; Yuan, Y.;  and Zhang, L.\n</span>\n\n  \n\n</span>\n\n   2026.\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://arxiv.org/abs/2605.30841\"\n     onclick=\"log_download('hu-xie-yuan-zhang-buptrbayesianunderdeterminedprojectiontrustregionmethodsforderivativefreeoptimization-2026', 'https://arxiv.org/abs/2605.30841', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"BUP-TR: Bayesian Underdetermined Projection Trust-Region Methods for Derivative-Free Optimization [link]\"\n       title=\"Paper\"\n       style=\"max-height: 1em;\"\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/hu-xie-yuan-zhang-buptrbayesianunderdeterminedprojectiontrustregionmethodsforderivativefreeoptimization-2026\"\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\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('hu-xie-yuan-zhang-buptrbayesianunderdeterminedprojectiontrustregionmethodsforderivativefreeoptimization-2026')\" -->\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</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@misc{hu-xie-yuan-zhang-2026-bup-tr,\n  author        = {Wei Hu and Pengcheng Xie and Ya-xiang Yuan and Li Zhang},\n  title         = {{BUP-TR}: {Bayesian} Underdetermined Projection Trust-Region Methods for Derivative-Free Optimization},\n  year          = {2026},\n  eprint        = {2605.30841},\n  archivePrefix = {arXiv},\n  primaryClass  = {math.OC},\n  url           = {https://arxiv.org/abs/2605.30841},\n  keywords      = {optimization}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"hu-xie-yuan-zhang-distributedgradientregularizednewtonmethodscheduledconsensusando1globaliterationcomplexity-2026\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://arxiv.org/abs/2605.19396\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'hu-xie-yuan-zhang-distributedgradientregularizednewtonmethodscheduledconsensusando1globaliterationcomplexity-2026', 'https://arxiv.org/abs/2605.19396', event);\">\n    Distributed Gradient-Regularized Newton Method: Scheduled Consensus and $O(ε^{-1})$ Global Iteration Complexity.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Hu, W.; <a class=\"bibbase author link\" href=\"https://pxie98.github.io/publication.html\">Xie, P.</a>; Yuan, Y.;  and Zhang, L.\n</span>\n\n  \n\n</span>\n\n   2026.\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://arxiv.org/abs/2605.19396\"\n     onclick=\"log_download('hu-xie-yuan-zhang-distributedgradientregularizednewtonmethodscheduledconsensusando1globaliterationcomplexity-2026', 'https://arxiv.org/abs/2605.19396', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Distributed Gradient-Regularized Newton Method: Scheduled Consensus and $O(ε^{-1})$ Global Iteration Complexity [link]\"\n       title=\"Paper\"\n       style=\"max-height: 1em;\"\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/hu-xie-yuan-zhang-distributedgradientregularizednewtonmethodscheduledconsensusando1globaliterationcomplexity-2026\"\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\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('hu-xie-yuan-zhang-distributedgradientregularizednewtonmethodscheduledconsensusando1globaliterationcomplexity-2026')\" -->\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</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@misc{hu-xie-yuan-zhang-2026-distributed-newton,\n  author        = {Wei Hu and Pengcheng Xie and Ya-xiang Yuan and Li Zhang},\n  title         = {Distributed Gradient-Regularized {Newton} Method: Scheduled Consensus and {$O(\\epsilon^{-1})$} Global Iteration Complexity},\n  year          = {2026},\n  eprint        = {2605.19396},\n  archivePrefix = {arXiv},\n  primaryClass  = {math.OC},\n  url           = {https://arxiv.org/abs/2605.19396},\n  keywords      = {optimization}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"xie-privacypreservingblackboxoptimizationpbbotheoryandthemodelbasedalgorithmdfop-2026\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://arxiv.org/abs/2601.11570\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'xie-privacypreservingblackboxoptimizationpbbotheoryandthemodelbasedalgorithmdfop-2026', 'https://arxiv.org/abs/2601.11570', event);\">\n    Privacy-Preserving Black-Box Optimization (PBBO): Theory and the Model-Based Algorithm DFOp.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://pxie98.github.io/publication.html\">Xie, P.</a>\n</span>\n\n  \n\n</span>\n\n   2026.\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://arxiv.org/abs/2601.11570\"\n     onclick=\"log_download('xie-privacypreservingblackboxoptimizationpbbotheoryandthemodelbasedalgorithmdfop-2026', 'https://arxiv.org/abs/2601.11570', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Privacy-Preserving Black-Box Optimization (PBBO): Theory and the Model-Based Algorithm DFOp [link]\"\n       title=\"Paper\"\n       style=\"max-height: 1em;\"\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/xie-privacypreservingblackboxoptimizationpbbotheoryandthemodelbasedalgorithmdfop-2026\"\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\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('xie-privacypreservingblackboxoptimizationpbbotheoryandthemodelbasedalgorithmdfop-2026')\" -->\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</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@misc{xie-2026-pbbo,\n  author        = {Pengcheng Xie},\n  title         = {Privacy-Preserving Black-Box Optimization ({PBBO}): Theory and the Model-Based Algorithm {DFOp}},\n  year          = {2026},\n  eprint        = {2601.11570},\n  archivePrefix = {arXiv},\n  primaryClass  = {cs.CR},\n  url           = {https://arxiv.org/abs/2601.11570},\n  keywords      = {optimization, privacy}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2025\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2025')\"\n      onkeypress=\"toggleGroup('group_2025')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2025</span>\n      <span class=\"bibbase_group_count\">\n        \n        (9)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"xie-yuan-anewderivativefreemethodusinganimprovedunderdeterminedquadraticinterpolationmodel-2025\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://doi.org/10.1137/23M1582023\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'xie-yuan-anewderivativefreemethodusinganimprovedunderdeterminedquadraticinterpolationmodel-2025', 'https://doi.org/10.1137/23M1582023', event);\">\n    A New Derivative-Free Method Using an Improved Underdetermined Quadratic Interpolation Model.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://pxie98.github.io/publication.html\">Xie, P.</a>;  and Yuan, Y.\n</span>\n\n  \n\n</span>\n\n  <i>SIAM Journal on Optimization</i>, 35(2): 1110–1133.  2025.\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://doi.org/10.1137/23M1582023\"\n     onclick=\"log_download('xie-yuan-anewderivativefreemethodusinganimprovedunderdeterminedquadraticinterpolationmodel-2025', 'https://doi.org/10.1137/23M1582023', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"A New Derivative-Free Method Using an Improved Underdetermined Quadratic Interpolation Model [link]\"\n       title=\"Paper\"\n       style=\"max-height: 1em;\"\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/10.1137/23M1582023\"\n     onclick=\"log_download('xie-yuan-anewderivativefreemethodusinganimprovedunderdeterminedquadraticinterpolationmodel-2025', 'http://doi.org/10.1137/23M1582023', 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-yuan-anewderivativefreemethodusinganimprovedunderdeterminedquadraticinterpolationmodel-2025\"\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\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('xie-yuan-anewderivativefreemethodusinganimprovedunderdeterminedquadraticinterpolationmodel-2025')\" -->\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</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{xie-yuan-2025-improved-underdetermined-model,\n  author  = {Pengcheng Xie and Ya-xiang Yuan},\n  title   = {A New Derivative-Free Method Using an Improved Underdetermined Quadratic Interpolation Model},\n  journal = {SIAM Journal on Optimization},\n  year    = {2025},\n  volume  = {35},\n  number  = {2},\n  pages   = {1110--1133},\n  doi     = {10.1137/23M1582023},\n  url     = {https://doi.org/10.1137/23M1582023},\n  keywords = {optimization}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"xie-sufficientconditionsforerrordistancereductionintheell2normtrustregionbetweenminimizersoflocalnonconvexmultivariatequadraticapproximates-2025\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://doi.org/10.1016/j.cam.2024.116146\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'xie-sufficientconditionsforerrordistancereductionintheell2normtrustregionbetweenminimizersoflocalnonconvexmultivariatequadraticapproximates-2025', 'https://doi.org/10.1016/j.cam.2024.116146', event);\">\n    Sufficient Conditions for Error Distance Reduction in the $\\ell_2$-Norm Trust Region Between Minimizers of Local Nonconvex Multivariate Quadratic Approximates.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://pxie98.github.io/publication.html\">Xie, P.</a>\n</span>\n\n  \n\n</span>\n\n  <i>Journal of Computational and Applied Mathematics</i>, 453: 116146.  2025.\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://doi.org/10.1016/j.cam.2024.116146\"\n     onclick=\"log_download('xie-sufficientconditionsforerrordistancereductionintheell2normtrustregionbetweenminimizersoflocalnonconvexmultivariatequadraticapproximates-2025', 'https://doi.org/10.1016/j.cam.2024.116146', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Sufficient Conditions for Error Distance Reduction in the $\\ell_2$-Norm Trust Region Between Minimizers of Local Nonconvex Multivariate Quadratic Approximates [link]\"\n       title=\"Paper\"\n       style=\"max-height: 1em;\"\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.cam.2024.116146\"\n     onclick=\"log_download('xie-sufficientconditionsforerrordistancereductionintheell2normtrustregionbetweenminimizersoflocalnonconvexmultivariatequadraticapproximates-2025', 'http://doi.org/10.1016/j.cam.2024.116146', 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-sufficientconditionsforerrordistancereductionintheell2normtrustregionbetweenminimizersoflocalnonconvexmultivariatequadraticapproximates-2025\"\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\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('xie-sufficientconditionsforerrordistancereductionintheell2normtrustregionbetweenminimizersoflocalnonconvexmultivariatequadraticapproximates-2025')\" -->\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</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{xie-2025-distance-reduction,\n  author  = {Pengcheng Xie},\n  title   = {Sufficient Conditions for Error Distance Reduction in the {$\\ell_2$}-Norm Trust Region Between Minimizers of Local Nonconvex Multivariate Quadratic Approximates},\n  journal = {Journal of Computational and Applied Mathematics},\n  year    = {2025},\n  volume  = {453},\n  pages   = {116146},\n  doi     = {10.1016/j.cam.2024.116146},\n  url     = {https://doi.org/10.1016/j.cam.2024.116146},\n  keywords = {optimization}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"xie-yuan-derivativefreeoptimizationwithtransformedobjectivefunctionsdfotoandthealgorithmbasedontheleastfrobeniusnormupdatingquadraticmodel-2025\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://doi.org/10.1007/s40305-023-00532-x\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'xie-yuan-derivativefreeoptimizationwithtransformedobjectivefunctionsdfotoandthealgorithmbasedontheleastfrobeniusnormupdatingquadraticmodel-2025', 'https://doi.org/10.1007/s40305-023-00532-x', event);\">\n    Derivative-Free Optimization with Transformed Objective Functions (DFOTO) and the Algorithm Based on the Least Frobenius Norm Updating Quadratic Model.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://pxie98.github.io/publication.html\">Xie, P.</a>;  and Yuan, Y.\n</span>\n\n  \n\n</span>\n\n  <i>Journal of the Operations Research Society of China</i>, 13: 327–363.  2025.\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://doi.org/10.1007/s40305-023-00532-x\"\n     onclick=\"log_download('xie-yuan-derivativefreeoptimizationwithtransformedobjectivefunctionsdfotoandthealgorithmbasedontheleastfrobeniusnormupdatingquadraticmodel-2025', 'https://doi.org/10.1007/s40305-023-00532-x', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Derivative-Free Optimization with Transformed Objective Functions (DFOTO) and the Algorithm Based on the Least Frobenius Norm Updating Quadratic Model [link]\"\n       title=\"Paper\"\n       style=\"max-height: 1em;\"\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/s40305-023-00532-x\"\n     onclick=\"log_download('xie-yuan-derivativefreeoptimizationwithtransformedobjectivefunctionsdfotoandthealgorithmbasedontheleastfrobeniusnormupdatingquadraticmodel-2025', 'http://doi.org/10.1007/s40305-023-00532-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/xie-yuan-derivativefreeoptimizationwithtransformedobjectivefunctionsdfotoandthealgorithmbasedontheleastfrobeniusnormupdatingquadraticmodel-2025\"\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\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('xie-yuan-derivativefreeoptimizationwithtransformedobjectivefunctionsdfotoandthealgorithmbasedontheleastfrobeniusnormupdatingquadraticmodel-2025')\" -->\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</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{xie-yuan-2025-dfoto,\n  author  = {Pengcheng Xie and Ya-xiang Yuan},\n  title   = {Derivative-Free Optimization with Transformed Objective Functions ({DFOTO}) and the Algorithm Based on the Least {Frobenius} Norm Updating Quadratic Model},\n  journal = {Journal of the Operations Research Society of China},\n  year    = {2025},\n  volume  = {13},\n  pages   = {327--363},\n  doi     = {10.1007/s40305-023-00532-x},\n  url     = {https://doi.org/10.1007/s40305-023-00532-x},\n  keywords = {optimization}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"li-zhou-xie-li-aspectrallevenbergmarquardtdeflationmethodformultiplesolutionsofsemilinearellipticsystems-2025\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://doi.org/10.1016/j.cam.2025.116998\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'li-zhou-xie-li-aspectrallevenbergmarquardtdeflationmethodformultiplesolutionsofsemilinearellipticsystems-2025', 'https://doi.org/10.1016/j.cam.2025.116998', event);\">\n    A Spectral Levenberg–Marquardt-Deflation Method for Multiple Solutions of Semilinear Elliptic Systems.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Li, L.; Zhou, Y.; <a class=\"bibbase author link\" href=\"https://pxie98.github.io/publication.html\">Xie, P.</a>;  and Li, H.\n</span>\n\n  \n\n</span>\n\n  <i>Journal of Computational and Applied Mathematics</i>, 475: 116998.  2025.\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://doi.org/10.1016/j.cam.2025.116998\"\n     onclick=\"log_download('li-zhou-xie-li-aspectrallevenbergmarquardtdeflationmethodformultiplesolutionsofsemilinearellipticsystems-2025', 'https://doi.org/10.1016/j.cam.2025.116998', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"A Spectral Levenberg–Marquardt-Deflation Method for Multiple Solutions of Semilinear Elliptic Systems [link]\"\n       title=\"Paper\"\n       style=\"max-height: 1em;\"\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.cam.2025.116998\"\n     onclick=\"log_download('li-zhou-xie-li-aspectrallevenbergmarquardtdeflationmethodformultiplesolutionsofsemilinearellipticsystems-2025', 'http://doi.org/10.1016/j.cam.2025.116998', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/li-zhou-xie-li-aspectrallevenbergmarquardtdeflationmethodformultiplesolutionsofsemilinearellipticsystems-2025\"\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\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('li-zhou-xie-li-aspectrallevenbergmarquardtdeflationmethodformultiplesolutionsofsemilinearellipticsystems-2025')\" -->\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</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{li-zhou-xie-li-2025-spectral-lm-deflation,\n  author  = {Lin Li and Yuheng Zhou and Pengcheng Xie and Huiyuan Li},\n  title   = {A Spectral {Levenberg--Marquardt}-Deflation Method for Multiple Solutions of Semilinear Elliptic Systems},\n  journal = {Journal of Computational and Applied Mathematics},\n  year    = {2025},\n  volume  = {475},\n  pages   = {116998},\n  doi     = {10.1016/j.cam.2025.116998},\n  url     = {https://doi.org/10.1016/j.cam.2025.116998},\n  keywords = {numerical PDE}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"ye-li-xie-yu-animprovedadaptiveorthogonalbasisdeflationmethodformultiplesolutionswithapplicationstononlinearellipticequationsinvaryingdomains-2025\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://doi.org/10.4208/jcm.2505-m2024-0276\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'ye-li-xie-yu-animprovedadaptiveorthogonalbasisdeflationmethodformultiplesolutionswithapplicationstononlinearellipticequationsinvaryingdomains-2025', 'https://doi.org/10.4208/jcm.2505-m2024-0276', event);\">\n    An Improved Adaptive Orthogonal Basis Deflation Method for Multiple Solutions with Applications to Nonlinear Elliptic Equations in Varying Domains.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Ye, Y.; Li, L.; <a class=\"bibbase author link\" href=\"https://pxie98.github.io/publication.html\">Xie, P.</a>;  and Yu, H.\n</span>\n\n  \n\n</span>\n\n  <i>Journal of Computational Mathematics</i>, 44(3): 794–818.  2025.\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://doi.org/10.4208/jcm.2505-m2024-0276\"\n     onclick=\"log_download('ye-li-xie-yu-animprovedadaptiveorthogonalbasisdeflationmethodformultiplesolutionswithapplicationstononlinearellipticequationsinvaryingdomains-2025', 'https://doi.org/10.4208/jcm.2505-m2024-0276', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"An Improved Adaptive Orthogonal Basis Deflation Method for Multiple Solutions with Applications to Nonlinear Elliptic Equations in Varying Domains [link]\"\n       title=\"Paper\"\n       style=\"max-height: 1em;\"\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/10.4208/jcm.2505-m2024-0276\"\n     onclick=\"log_download('ye-li-xie-yu-animprovedadaptiveorthogonalbasisdeflationmethodformultiplesolutionswithapplicationstononlinearellipticequationsinvaryingdomains-2025', 'http://doi.org/10.4208/jcm.2505-m2024-0276', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/ye-li-xie-yu-animprovedadaptiveorthogonalbasisdeflationmethodformultiplesolutionswithapplicationstononlinearellipticequationsinvaryingdomains-2025\"\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\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('ye-li-xie-yu-animprovedadaptiveorthogonalbasisdeflationmethodformultiplesolutionswithapplicationstononlinearellipticequationsinvaryingdomains-2025')\" -->\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</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{ye-li-xie-yu-2025-adaptive-deflation,\n  author  = {Yangyi Ye and Lin Li and Pengcheng Xie and Haijun Yu},\n  title   = {An Improved Adaptive Orthogonal Basis Deflation Method for Multiple Solutions with Applications to Nonlinear Elliptic Equations in Varying Domains},\n  journal = {Journal of Computational Mathematics},\n  year    = {2025},\n  volume  = {44},\n  number  = {3},\n  pages   = {794--818},\n  doi     = {10.4208/jcm.2505-m2024-0276},\n  url     = {https://doi.org/10.4208/jcm.2505-m2024-0276},\n  keywords = {numerical PDE}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"dzahini-wild-xie-optimizationapproachesforsolvinginverseproblemsunderuncertainty-2025\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://www.orau.gov/support_files/2025InverseMethods/WildS.pdf\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'dzahini-wild-xie-optimizationapproachesforsolvinginverseproblemsunderuncertainty-2025', 'https://www.orau.gov/support_files/2025InverseMethods/WildS.pdf', event);\">\n    Optimization Approaches for Solving Inverse Problems Under Uncertainty.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Dzahini, K. J.; Wild, S. M.;  and <a class=\"bibbase author link\" href=\"https://pxie98.github.io/publication.html\">Xie, P.</a>\n</span>\n\n  \n\n</span>\n\n  <i>Inverse Methods for Complex Systems under Uncertainty Workshop</i>.  2025.\n  <span class=\"note\">Position paper, U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research</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://www.orau.gov/support_files/2025InverseMethods/WildS.pdf\"\n     onclick=\"log_download('dzahini-wild-xie-optimizationapproachesforsolvinginverseproblemsunderuncertainty-2025', 'https://www.orau.gov/support_files/2025InverseMethods/WildS.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Optimization Approaches for Solving Inverse Problems Under Uncertainty [pdf]\"\n       title=\"Paper\"\n       style=\"max-height: 1em;\"\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/dzahini-wild-xie-optimizationapproachesforsolvinginverseproblemsunderuncertainty-2025\"\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\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('dzahini-wild-xie-optimizationapproachesforsolvinginverseproblemsunderuncertainty-2025')\" -->\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</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{dzahini-wild-xie-2025-inverse-problems,\n  author  = {Kwassi J. Dzahini and Stefan M. Wild and Pengcheng Xie},\n  title   = {Optimization Approaches for Solving Inverse Problems Under Uncertainty},\n  journal = {Inverse Methods for Complex Systems under Uncertainty Workshop},\n  year    = {2025},\n  note    = {Position paper, U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research},\n  url     = {https://www.orau.gov/support_files/2025InverseMethods/WildS.pdf},\n  keywords = {optimization}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"li-xie-zhang-anovelnumericalmethodtailoredforunconstrainedoptimizationproblems-2025\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://arxiv.org/abs/2504.02832\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'li-xie-zhang-anovelnumericalmethodtailoredforunconstrainedoptimizationproblems-2025', 'https://arxiv.org/abs/2504.02832', event);\">\n    A Novel Numerical Method Tailored for Unconstrained Optimization Problems.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Li, L.; <a class=\"bibbase author link\" href=\"https://pxie98.github.io/publication.html\">Xie, P.</a>;  and Zhang, L.\n</span>\n\n  \n\n</span>\n\n   2025.\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://arxiv.org/abs/2504.02832\"\n     onclick=\"log_download('li-xie-zhang-anovelnumericalmethodtailoredforunconstrainedoptimizationproblems-2025', 'https://arxiv.org/abs/2504.02832', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"A Novel Numerical Method Tailored for Unconstrained Optimization Problems [link]\"\n       title=\"Paper\"\n       style=\"max-height: 1em;\"\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/li-xie-zhang-anovelnumericalmethodtailoredforunconstrainedoptimizationproblems-2025\"\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\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>7 downloads</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('li-xie-zhang-anovelnumericalmethodtailoredforunconstrainedoptimizationproblems-2025')\" -->\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</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@misc{li-xie-zhang-2025-novel-numerical-method,\n  author        = {Lin Li and Pengcheng Xie and Li Zhang},\n  title         = {A Novel Numerical Method Tailored for Unconstrained Optimization Problems},\n  year          = {2025},\n  eprint        = {2504.02832},\n  archivePrefix = {arXiv},\n  primaryClass  = {math.OC},\n  url           = {https://arxiv.org/abs/2504.02832},\n  keywords      = {optimization}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"xie-zhou-zhou-objectivevaluechangeandshapebasedacceleratedoptimizationforneuralnetworkapproximation-2025\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://arxiv.org/abs/2508.20290\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'xie-zhou-zhou-objectivevaluechangeandshapebasedacceleratedoptimizationforneuralnetworkapproximation-2025', 'https://arxiv.org/abs/2508.20290', event);\">\n    Objective Value Change and Shape-Based Accelerated Optimization for Neural Network Approximation.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://pxie98.github.io/publication.html\">Xie, P.</a>; Zhou, Z.;  and Zhou, Z.\n</span>\n\n  \n\n</span>\n\n   2025.\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://arxiv.org/abs/2508.20290\"\n     onclick=\"log_download('xie-zhou-zhou-objectivevaluechangeandshapebasedacceleratedoptimizationforneuralnetworkapproximation-2025', 'https://arxiv.org/abs/2508.20290', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Objective Value Change and Shape-Based Accelerated Optimization for Neural Network Approximation [link]\"\n       title=\"Paper\"\n       style=\"max-height: 1em;\"\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/xie-zhou-zhou-objectivevaluechangeandshapebasedacceleratedoptimizationforneuralnetworkapproximation-2025\"\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\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('xie-zhou-zhou-objectivevaluechangeandshapebasedacceleratedoptimizationforneuralnetworkapproximation-2025')\" -->\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</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@misc{xie-zhou-zhou-2025-shape-based-optimization,\n  author        = {Pengcheng Xie and Zihao Zhou and Zijian Zhou},\n  title         = {Objective Value Change and Shape-Based Accelerated Optimization for Neural Network Approximation},\n  year          = {2025},\n  eprint        = {2508.20290},\n  archivePrefix = {arXiv},\n  primaryClass  = {cs.LG},\n  url           = {https://arxiv.org/abs/2508.20290},\n  keywords      = {machine learning, optimization}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"he-xie-modeldrivensubspacesforlargescaleoptimizationwithlocalapproximationstrategy-2025\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://arxiv.org/abs/2509.08256\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'he-xie-modeldrivensubspacesforlargescaleoptimizationwithlocalapproximationstrategy-2025', 'https://arxiv.org/abs/2509.08256', event);\">\n    Model-Driven Subspaces for Large-Scale Optimization with Local Approximation Strategy.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  He, Y.;  and <a class=\"bibbase author link\" href=\"https://pxie98.github.io/publication.html\">Xie, P.</a>\n</span>\n\n  \n\n</span>\n\n   2025.\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://arxiv.org/abs/2509.08256\"\n     onclick=\"log_download('he-xie-modeldrivensubspacesforlargescaleoptimizationwithlocalapproximationstrategy-2025', 'https://arxiv.org/abs/2509.08256', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Model-Driven Subspaces for Large-Scale Optimization with Local Approximation Strategy [link]\"\n       title=\"Paper\"\n       style=\"max-height: 1em;\"\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/he-xie-modeldrivensubspacesforlargescaleoptimizationwithlocalapproximationstrategy-2025\"\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\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('he-xie-modeldrivensubspacesforlargescaleoptimizationwithlocalapproximationstrategy-2025')\" -->\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</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@misc{he-xie-2025-model-driven-subspaces,\n  author        = {Yitong He and Pengcheng Xie},\n  title         = {Model-Driven Subspaces for Large-Scale Optimization with Local Approximation Strategy},\n  year          = {2025},\n  eprint        = {2509.08256},\n  archivePrefix = {arXiv},\n  primaryClass  = {math.OC},\n  url           = {https://arxiv.org/abs/2509.08256},\n  keywords      = {optimization}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2024\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2024')\"\n      onkeypress=\"toggleGroup('group_2024')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2024</span>\n      <span class=\"bibbase_group_count\">\n        \n        (7)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"xie-themodelingandoptimizationofamultidamsystem-2024\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://doi.org/10.11648/j.acm.20241305.13\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'xie-themodelingandoptimizationofamultidamsystem-2024', 'https://doi.org/10.11648/j.acm.20241305.13', event);\">\n    The Modeling and Optimization of a Multi-Dam System.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://pxie98.github.io/publication.html\">Xie, P.</a>\n</span>\n\n  \n\n</span>\n\n  <i>Applied and Computational Mathematics</i>, 13(5): 140–152.  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://doi.org/10.11648/j.acm.20241305.13\"\n     onclick=\"log_download('xie-themodelingandoptimizationofamultidamsystem-2024', 'https://doi.org/10.11648/j.acm.20241305.13', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"The Modeling and Optimization of a Multi-Dam System [link]\"\n       title=\"Paper\"\n       style=\"max-height: 1em;\"\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/10.11648/j.acm.20241305.13\"\n     onclick=\"log_download('xie-themodelingandoptimizationofamultidamsystem-2024', 'http://doi.org/10.11648/j.acm.20241305.13', 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-themodelingandoptimizationofamultidamsystem-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\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('xie-themodelingandoptimizationofamultidamsystem-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</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{xie-2024-multidam,\n  author  = {Pengcheng Xie},\n  title   = {The Modeling and Optimization of a Multi-Dam System},\n  journal = {Applied and Computational Mathematics},\n  year    = {2024},\n  volume  = {13},\n  number  = {5},\n  pages   = {140--152},\n  doi     = {10.11648/j.acm.20241305.13},\n  url     = {https://doi.org/10.11648/j.acm.20241305.13},\n  keywords = {optimization}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"xie-ontherelationshipbetweenpoisednessinderivativefreeoptimizationandoutliersinlocaloutlierfactor-2024\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://arxiv.org/abs/2407.17529\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'xie-ontherelationshipbetweenpoisednessinderivativefreeoptimizationandoutliersinlocaloutlierfactor-2024', 'https://arxiv.org/abs/2407.17529', event);\">\n    On the Relationship Between $Λ$-Poisedness in Derivative-Free Optimization and Outliers in Local Outlier Factor.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://pxie98.github.io/publication.html\">Xie, P.</a>\n</span>\n\n  \n\n</span>\n\n   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://arxiv.org/abs/2407.17529\"\n     onclick=\"log_download('xie-ontherelationshipbetweenpoisednessinderivativefreeoptimizationandoutliersinlocaloutlierfactor-2024', 'https://arxiv.org/abs/2407.17529', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"On the Relationship Between $Λ$-Poisedness in Derivative-Free Optimization and Outliers in Local Outlier Factor [link]\"\n       title=\"Paper\"\n       style=\"max-height: 1em;\"\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/xie-ontherelationshipbetweenpoisednessinderivativefreeoptimizationandoutliersinlocaloutlierfactor-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\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>4 downloads</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('xie-ontherelationshipbetweenpoisednessinderivativefreeoptimizationandoutliersinlocaloutlierfactor-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</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@misc{xie-2024-lambda-poisedness-lof,\n  author        = {Pengcheng Xie},\n  title         = {On the Relationship Between {$\\Lambda$}-Poisedness in Derivative-Free Optimization and Outliers in Local Outlier Factor},\n  year          = {2024},\n  eprint        = {2407.17529},\n  archivePrefix = {arXiv},\n  primaryClass  = {math.OC},\n  url           = {https://arxiv.org/abs/2407.17529},\n  keywords      = {optimization, approximation}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"xie-wild-barycenteroftheweightcoefficientregionofleastweightedh2normupdatingquadraticmodelswithvanishingtrustregionradius-2024\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  Barycenter of the Weight-Coefficient Region of Least-Weighted $H^2$ Norm Updating Quadratic Models with Vanishing Trust-Region Radius.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://pxie98.github.io/publication.html\">Xie, P.</a>;  and Wild, S. M.\n</span>\n\n  \n\n</span>\n\n   2024.\n  <span class=\"note\">SIAM Northern and Central California Sectional Conference (NCC24), Early Career Travel Award</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\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/xie-wild-barycenteroftheweightcoefficientregionofleastweightedh2normupdatingquadraticmodelswithvanishingtrustregionradius-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\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('xie-wild-barycenteroftheweightcoefficientregionofleastweightedh2normupdatingquadraticmodelswithvanishingtrustregionradius-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</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@misc{xie-wild-2024-h2-barycenter,\n  author   = {Pengcheng Xie and Stefan M. Wild},\n  title    = {Barycenter of the Weight-Coefficient Region of Least-Weighted {$H^2$} Norm Updating Quadratic Models with Vanishing Trust-Region Radius},\n  year     = {2024},\n  note     = {SIAM Northern and Central California Sectional Conference (NCC24), Early Career Travel Award},\n  keywords = {optimization}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"xie-others-anovellocalanalysisofobjectivesapproximatedbyneuralnetworkslchange-2024\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  A Novel Local Analysis of Objectives Approximated by Neural Networks: L-Change.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://pxie98.github.io/publication.html\">Xie, P.</a>;  and others\n</span>\n\n  \n\n</span>\n\n   2024.\n  <span class=\"note\">International Conference on Mathematical Theory of Deep Learning (MTDL)</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\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/xie-others-anovellocalanalysisofobjectivesapproximatedbyneuralnetworkslchange-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\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('xie-others-anovellocalanalysisofobjectivesapproximatedbyneuralnetworkslchange-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</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@misc{xie-etal-2024-l-change,\n  author   = {Pengcheng Xie and others},\n  title    = {A Novel Local Analysis of Objectives Approximated by Neural Networks: {L-Change}},\n  year     = {2024},\n  note     = {International Conference on Mathematical Theory of Deep Learning (MTDL)},\n  keywords = {machine learning, neural network}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"hu-xie-zhang-yuan-alowcomputationcostcubicregularizedquasinewtonmethodfordistributedoptimizationlc3rqn-2024\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://lsec.cc.ac.cn/~moa2024/Poster_List.pdf\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'hu-xie-zhang-yuan-alowcomputationcostcubicregularizedquasinewtonmethodfordistributedoptimizationlc3rqn-2024', 'https://lsec.cc.ac.cn/~moa2024/Poster_List.pdf', event);\">\n    A Low-Computation-Cost Cubic-Regularized Quasi-Newton Method for Distributed Optimization: LC3RQN.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Hu, W.; <a class=\"bibbase author link\" href=\"https://pxie98.github.io/publication.html\">Xie, P.</a>; Zhang, L.;  and Yuan, Y.\n</span>\n\n  \n\n</span>\n\n   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://lsec.cc.ac.cn/~moa2024/Poster_List.pdf\"\n     onclick=\"log_download('hu-xie-zhang-yuan-alowcomputationcostcubicregularizedquasinewtonmethodfordistributedoptimizationlc3rqn-2024', 'https://lsec.cc.ac.cn/~moa2024/Poster_List.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"A Low-Computation-Cost Cubic-Regularized Quasi-Newton Method for Distributed Optimization: LC3RQN [pdf]\"\n       title=\"Paper\"\n       style=\"max-height: 1em;\"\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/hu-xie-zhang-yuan-alowcomputationcostcubicregularizedquasinewtonmethodfordistributedoptimizationlc3rqn-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\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>29 downloads</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('hu-xie-zhang-yuan-alowcomputationcostcubicregularizedquasinewtonmethodfordistributedoptimizationlc3rqn-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</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@misc{hu-xie-zhang-yuan-2024-lc3rqn,\n  author   = {Wei Hu and Pengcheng Xie and Li Zhang and Ya-xiang Yuan},\n  title    = {A Low-Computation-Cost Cubic-Regularized Quasi-{Newton} Method for Distributed Optimization: {LC3RQN}},\n  year     = {2024},\n  url      = {https://lsec.cc.ac.cn/~moa2024/Poster_List.pdf},\n  keywords = {optimization}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"xie-anefficientderivativefreemethodforfindingmultiplesolutions-2024\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  An Efficient Derivative-Free Method for Finding Multiple Solutions.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://pxie98.github.io/publication.html\">Xie, P.</a>\n</span>\n\n  \n\n</span>\n\n   2024.\n  <span class=\"note\">Manuscript</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\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/xie-anefficientderivativefreemethodforfindingmultiplesolutions-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\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('xie-anefficientderivativefreemethodforfindingmultiplesolutions-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</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@misc{xie-2024-multiple-solutions,\n  author   = {Pengcheng Xie},\n  title    = {An Efficient Derivative-Free Method for Finding Multiple Solutions},\n  year     = {2024},\n  note     = {Manuscript},\n  keywords = {numerical PDE}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"xie-anoteontheinvariantdistributionofastochasticdynamicalsystem-2024\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4910398\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'xie-anoteontheinvariantdistributionofastochasticdynamicalsystem-2024', 'https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4910398', event);\">\n    A Note on the Invariant Distribution of a Stochastic Dynamical System.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://pxie98.github.io/publication.html\">Xie, P.</a>\n</span>\n\n  \n\n</span>\n\n   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://papers.ssrn.com/sol3/papers.cfm?abstract_id=4910398\"\n     onclick=\"log_download('xie-anoteontheinvariantdistributionofastochasticdynamicalsystem-2024', 'https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4910398', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"A Note on the Invariant Distribution of a Stochastic Dynamical System [link]\"\n       title=\"Paper\"\n       style=\"max-height: 1em;\"\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/10.12074/202304.01048\"\n     onclick=\"log_download('xie-anoteontheinvariantdistributionofastochasticdynamicalsystem-2024', 'http://doi.org/10.12074/202304.01048', 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-anoteontheinvariantdistributionofastochasticdynamicalsystem-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\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('xie-anoteontheinvariantdistributionofastochasticdynamicalsystem-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</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@misc{xie-2024-invariant-distribution,\n  author   = {Pengcheng Xie},\n  title    = {A Note on the Invariant Distribution of a Stochastic Dynamical System},\n  year     = {2024},\n  doi      = {10.12074/202304.01048},\n  url      = {https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4910398},\n  keywords = {control}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2023\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2023')\"\n      onkeypress=\"toggleGroup('group_2023')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2023</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=\"xie-yuan-aderivativefreeoptimizationalgorithmcombininglinesearchandtrustregiontechniques-2023\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://doi.org/10.1007/s11401-023-0040-y\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'xie-yuan-aderivativefreeoptimizationalgorithmcombininglinesearchandtrustregiontechniques-2023', 'https://doi.org/10.1007/s11401-023-0040-y', event);\">\n    A Derivative-Free Optimization Algorithm Combining Line-Search and Trust-Region Techniques.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://pxie98.github.io/publication.html\">Xie, P.</a>;  and Yuan, Y.\n</span>\n\n  \n\n</span>\n\n  <i>Chinese Annals of Mathematics, Series B</i>, 44(5): 693–708.  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://doi.org/10.1007/s11401-023-0040-y\"\n     onclick=\"log_download('xie-yuan-aderivativefreeoptimizationalgorithmcombininglinesearchandtrustregiontechniques-2023', 'https://doi.org/10.1007/s11401-023-0040-y', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"A Derivative-Free Optimization Algorithm Combining Line-Search and Trust-Region Techniques [link]\"\n       title=\"Paper\"\n       style=\"max-height: 1em;\"\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/s11401-023-0040-y\"\n     onclick=\"log_download('xie-yuan-aderivativefreeoptimizationalgorithmcombininglinesearchandtrustregiontechniques-2023', 'http://doi.org/10.1007/s11401-023-0040-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/xie-yuan-aderivativefreeoptimizationalgorithmcombininglinesearchandtrustregiontechniques-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\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>5 downloads</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('xie-yuan-aderivativefreeoptimizationalgorithmcombininglinesearchandtrustregiontechniques-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</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{xie-yuan-2023-line-search-trust-region,\n  author  = {Pengcheng Xie and Ya-xiang Yuan},\n  title   = {A Derivative-Free Optimization Algorithm Combining Line-Search and Trust-Region Techniques},\n  journal = {Chinese Annals of Mathematics, Series B},\n  year    = {2023},\n  volume  = {44},\n  number  = {5},\n  pages   = {693--708},\n  doi     = {10.1007/s11401-023-0040-y},\n  url     = {https://doi.org/10.1007/s11401-023-0040-y},\n  keywords = {optimization}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"xie-aderivativefreetrustregionmethodforoptimizationontheellipsoid-2023\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://doi.org/10.1088/1742-6596/2620/1/012007\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'xie-aderivativefreetrustregionmethodforoptimizationontheellipsoid-2023', 'https://doi.org/10.1088/1742-6596/2620/1/012007', event);\">\n    A Derivative-Free Trust-Region Method for Optimization on the Ellipsoid.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://pxie98.github.io/publication.html\">Xie, P.</a>\n</span>\n\n  \n\n</span>\n\n  <i>Journal of Physics: Conference Series</i>, 2620: 012007.  2023.\n  <span class=\"note\">Presented at the 2023 International Conference on Advances in Computer Science and Engineering Technology</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://doi.org/10.1088/1742-6596/2620/1/012007\"\n     onclick=\"log_download('xie-aderivativefreetrustregionmethodforoptimizationontheellipsoid-2023', 'https://doi.org/10.1088/1742-6596/2620/1/012007', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"A Derivative-Free Trust-Region Method for Optimization on the Ellipsoid [link]\"\n       title=\"Paper\"\n       style=\"max-height: 1em;\"\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/10.1088/1742-6596/2620/1/012007\"\n     onclick=\"log_download('xie-aderivativefreetrustregionmethodforoptimizationontheellipsoid-2023', 'http://doi.org/10.1088/1742-6596/2620/1/012007', 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-aderivativefreetrustregionmethodforoptimizationontheellipsoid-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\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>4 downloads</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('xie-aderivativefreetrustregionmethodforoptimizationontheellipsoid-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</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{xie-2023-ellipsoid,\n  author  = {Pengcheng Xie},\n  title   = {A Derivative-Free Trust-Region Method for Optimization on the Ellipsoid},\n  journal = {Journal of Physics: Conference Series},\n  year    = {2023},\n  volume  = {2620},\n  pages   = {012007},\n  doi     = {10.1088/1742-6596/2620/1/012007},\n  url     = {https://doi.org/10.1088/1742-6596/2620/1/012007},\n  note    = {Presented at the 2023 International Conference on Advances in Computer Science and Engineering Technology},\n  keywords = {optimization}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2021\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2021')\"\n      onkeypress=\"toggleGroup('group_2021')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2021</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=\"li-xie-zhou-others-simulationofinteractionoffoldedwaveguidespacetravelingwavetubeswithderivativefreemixedintegerbasednewuoaalgorithm-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://doi.org/10.1109/ICCC54389.2021.9674410\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'li-xie-zhou-others-simulationofinteractionoffoldedwaveguidespacetravelingwavetubeswithderivativefreemixedintegerbasednewuoaalgorithm-2021', 'https://doi.org/10.1109/ICCC54389.2021.9674410', event);\">\n    Simulation of Interaction of Folded Waveguide Space Traveling Wave Tubes with Derivative-Free Mixed-Integer-Based NEWUOA Algorithm.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Li, S.; <a class=\"bibbase author link\" href=\"https://pxie98.github.io/publication.html\">Xie, P.</a>; Zhou, Z.;  and others\n</span>\n\n  \n\n</span>\n\n  In <i>2021 7th International Conference on Computer and Communications (ICCC)</i>, pages 1215–1219,  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://doi.org/10.1109/ICCC54389.2021.9674410\"\n     onclick=\"log_download('li-xie-zhou-others-simulationofinteractionoffoldedwaveguidespacetravelingwavetubeswithderivativefreemixedintegerbasednewuoaalgorithm-2021', 'https://doi.org/10.1109/ICCC54389.2021.9674410', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Simulation of Interaction of Folded Waveguide Space Traveling Wave Tubes with Derivative-Free Mixed-Integer-Based NEWUOA Algorithm [link]\"\n       title=\"Paper\"\n       style=\"max-height: 1em;\"\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/10.1109/ICCC54389.2021.9674410\"\n     onclick=\"log_download('li-xie-zhou-others-simulationofinteractionoffoldedwaveguidespacetravelingwavetubeswithderivativefreemixedintegerbasednewuoaalgorithm-2021', 'http://doi.org/10.1109/ICCC54389.2021.9674410', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/li-xie-zhou-others-simulationofinteractionoffoldedwaveguidespacetravelingwavetubeswithderivativefreemixedintegerbasednewuoaalgorithm-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\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('li-xie-zhou-others-simulationofinteractionoffoldedwaveguidespacetravelingwavetubeswithderivativefreemixedintegerbasednewuoaalgorithm-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</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@inproceedings{li-xie-zhou-etal-2021-newuoa,\n  author    = {Shuoran Li and Pengcheng Xie and Zihao Zhou and others},\n  title     = {Simulation of Interaction of Folded Waveguide Space Traveling Wave Tubes with Derivative-Free Mixed-Integer-Based {NEWUOA} Algorithm},\n  booktitle = {2021 7th International Conference on Computer and Communications (ICCC)},\n  year      = {2021},\n  pages     = {1215--1219},\n  doi       = {10.1109/ICCC54389.2021.9674410},\n  url       = {https://doi.org/10.1109/ICCC54389.2021.9674410},\n  keywords  = {optimization}\n}\n</pre>\n</div>\n\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2019\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2019')\"\n      onkeypress=\"toggleGroup('group_2019')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2019</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-tao-parametricresonantcontrolofmacroscopicbehaviorsofmultipleoscillators-2019\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://doi.org/10.23919/ACC.2019.8814709\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'xie-tao-parametricresonantcontrolofmacroscopicbehaviorsofmultipleoscillators-2019', 'https://doi.org/10.23919/ACC.2019.8814709', event);\">\n    Parametric Resonant Control of Macroscopic Behaviors of Multiple Oscillators.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://pxie98.github.io/publication.html\">Xie, P.</a>;  and Tao, M.\n</span>\n\n  \n\n</span>\n\n  In <i>2019 American Control Conference (ACC)</i>, pages 1898–1905,  2019. \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://doi.org/10.23919/ACC.2019.8814709\"\n     onclick=\"log_download('xie-tao-parametricresonantcontrolofmacroscopicbehaviorsofmultipleoscillators-2019', 'https://doi.org/10.23919/ACC.2019.8814709', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Parametric Resonant Control of Macroscopic Behaviors of Multiple Oscillators [link]\"\n       title=\"Paper\"\n       style=\"max-height: 1em;\"\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/10.23919/ACC.2019.8814709\"\n     onclick=\"log_download('xie-tao-parametricresonantcontrolofmacroscopicbehaviorsofmultipleoscillators-2019', 'http://doi.org/10.23919/ACC.2019.8814709', 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-tao-parametricresonantcontrolofmacroscopicbehaviorsofmultipleoscillators-2019\"\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\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>5 downloads</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('xie-tao-parametricresonantcontrolofmacroscopicbehaviorsofmultipleoscillators-2019')\" -->\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</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@inproceedings{xie-tao-2019-acc,\n  author    = {Pengcheng Xie and Molei Tao},\n  title     = {Parametric Resonant Control of Macroscopic Behaviors of Multiple Oscillators},\n  booktitle = {2019 American Control Conference (ACC)},\n  year      = {2019},\n  pages     = {1898--1905},\n  doi       = {10.23919/ACC.2019.8814709},\n  url       = {https://doi.org/10.23919/ACC.2019.8814709},\n  keywords  = {control}\n}\n\n</pre>\n</div>\n\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"}; 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