Modified subgradient extragradient algorithms for systems of generalized equilibria with constraints

Lu-Chuan Ceng; Li-Jun Zhu; Tzu-Chien Yin; Lu-Chuan Ceng; Li-Jun Zhu; Tzu-Chien Yin

doi:10.3934/math.2023154

AIMS Mathematics

2023, Volume 8, Issue 2: 2961-2994. doi: 10.3934/math.2023154

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Modified subgradient extragradient algorithms for systems of generalized equilibria with constraints

1.
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
2.
The Key Laboratory of Intelligent Information and Big Data Processing of NingXia, North Minzu University, Yinchuan 750021, China
3.
Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan

Received: 15 June 2022 Revised: 22 October 2022 Accepted: 09 November 2022 Published: 14 November 2022
MSC : 47H09, 47H10, 47J20, 47J25

In this paper, we introduce the modified Mann-like subgradient-like extragradient implicit rules with linear-search process for finding a common solution of a system of generalized equilibrium problems, a pseudomonotone variational inequality problem and a fixed-point problem of an asymptotically nonexpansive mapping in a real Hilbert space. The proposed algorithms are based on the subgradient extragradient rule with linear-search process, Mann implicit iteration approach, and hybrid deepest-descent technique. Under mild restrictions, we demonstrate the strong convergence of the proposed algorithms to a common solution of the investigated problems, which is a unique solution of a certain hierarchical variational inequality defined on their common solution set.
- system of generalized equilibrium problems,
- variational inequality,
- subgradient extragradient method,
- fixed point,
- convergence
Citation: Lu-Chuan Ceng, Li-Jun Zhu, Tzu-Chien Yin. Modified subgradient extragradient algorithms for systems of generalized equilibria with constraints[J]. AIMS Mathematics, 2023, 8(2): 2961-2994. doi: 10.3934/math.2023154

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Abstract

In this paper, we introduce the modified Mann-like subgradient-like extragradient implicit rules with linear-search process for finding a common solution of a system of generalized equilibrium problems, a pseudomonotone variational inequality problem and a fixed-point problem of an asymptotically nonexpansive mapping in a real Hilbert space. The proposed algorithms are based on the subgradient extragradient rule with linear-search process, Mann implicit iteration approach, and hybrid deepest-descent technique. Under mild restrictions, we demonstrate the strong convergence of the proposed algorithms to a common solution of the investigated problems, which is a unique solution of a certain hierarchical variational inequality defined on their common solution set.

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