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Self-Adaptive Extragradient Algorithms for Quasi-Equilibrium Problems

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Abstract

We propose two iterative algorithms for solving two classes of quasi-equilibrium problems in Hilbert spaces: pseudomonotone and quasimonotone ones. The algorithms combine the subgradient method and the projection method with self-adaptive step sizes. Convergence of our proposed algorithms requires a condition that is milder than the one commonly used in the existing papers. Numerical experiments show that our algorithms are efficient and competitive to other extragradient-type, projection-type, and proximal point algorithms in solving the problem.

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Acknowledgements

The authors are extremely grateful to the editor and anonymous reviewers for their valuable comments and suggestions, which have helped improve the quality of the paper. This research was supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.02–2023.01 (Tran Van Thang). Part of this work was done during a research stay of the second author (Xuan Thanh Le) at Vietnam Institute for Advanced Study in Mathematics.

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Authors and Affiliations

  1. Electric Power University, 235 Hoang Quoc Viet, Bac Tu Liem, Hanoi, Vietnam

    Tran Van Thang

  2. Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam

    Xuan Thanh Le

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  1. Tran Van Thang
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Correspondence to Tran Van Thang.

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Communicated by Juan-Enrique Martinez Legaz.

Dedicated to Professor Le Dung Muu on the occasion of his 75th birthday.

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Van Thang, T., Le, X.T. Self-Adaptive Extragradient Algorithms for Quasi-Equilibrium Problems. J Optim Theory Appl (2024). https://doi.org/10.1007/s10957-024-02555-7

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