Modified subgradient extragradient algorithms for systems of generalized equilibria with constraints

• Published in: AIMS mathematics Vol. 8; no. 2; pp. 2961 - 2994
• Main Authors: Ceng, Lu-Chuan, Zhu, Li-Jun, Yin, Tzu-Chien
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2023
• Subjects: convergence; fixed point; subgradient extragradient method; system of generalized equilibrium problems; variational inequality
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2023154

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.