Modified subgradient extragradient algorithms for systems of generalized equilibria with constraints

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.

Keywords

• system of generalized equilibrium problems
• variational inequality
• subgradient extragradient method
• fixed point
• convergence