Parallel hybrid extragradient methods for pseudomonotone equilibrium problems and nonexpansive mappings

TL;DR

This paper introduces three parallel hybrid extragradient algorithms designed to efficiently find common solutions to equilibrium problems involving pseudomonotone bifunctions and fixed points of nonexpansive mappings in Hilbert spaces, reducing computational effort.

Contribution

The paper develops and analyzes novel parallel hybrid extragradient methods for solving combined equilibrium and fixed point problems, enhancing computational efficiency.

Findings

Algorithms successfully find common solutions in numerical tests.

Parallel methods reduce computational effort compared to sequential approaches.

Numerical example demonstrates effectiveness of the proposed algorithms.

Abstract

In this paper we propose and analyze three parallel hybrid extragradient methods for finding a common element of the set of solutions of equilibrium problems involving pseudomonotone bifunctions and the set of fixed points of nonexpansive mappings in a real Hilbert space. Based on parallel computation we can reduce the overall computational effort under widely used conditions on the bifunctions and the nonexpansive mappings.A simple numerical example is given to illustrate the proposed parallel algorithms.