Modified subgradient extragradient algorithms for systems of generalized equilibria with constraints

AIMS Mathematics

article

Lu-Chuan Ceng¹  Li-Jun Zhu²  Tzu-Chien Yin³ 

[1] Department of Mathematics, Shanghai Normal University;The Key Laboratory of Intelligent Information and Big Data Processing of NingXia, North Minzu University, Yinchuan 750021;Research Center for Interneural Computing, China Medical University Hospital, China Medical University

关键词: system of generalized equilibrium problems;    variational inequality;    subgradient extragradient method;    fixed point;    convergence;   

DOI  :  10.3934/math.2023154

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

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.

【 授权许可】

CC BY