Self-Adaptive Extragradient Algorithms for Quasi-Equilibrium Problems

Tran Thang () and Xuan Thanh Le ()
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Tran Thang: Electric Power University
Xuan Thanh Le: Vietnam Academy of Science and Technology

Journal of Optimization Theory and Applications, 2024, vol. 203, issue 3, No 30, 2988-3013

Abstract: 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.

Keywords: Quasi-equilibrium problem; Fixed point; Pseudomonotonicity; Quasimonotonicity; Extragradient projection method (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02555-7

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