Self adaptive inertial extragradient algorithms for solving bilevel pseudomonotone variational inequality problems. Tan, B., Liu, L., & Qin, X. *Japan Journal of Industrial and Applied Mathematics*, 38(2):519-543, 2021. (~~ESI Highly Cited Paper~~)

Paper doi abstract bibtex

Paper doi abstract bibtex

We introduce two inertial extragradient algorithms for solving a bilevel pseudomonotone variational inequality problem in real Hilbert spaces. The advantages of the proposed algorithms are that they can work without the prior knowledge of the Lipschitz constant of the involving operator and only one projection onto the feasible set is required. Strong convergence theorems of the suggested algorithms are obtained under suitable conditions. Finally, some numerical examples are provided to show the efficiency of the proposed algorithms.

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

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