A relaxed proximal point algorithm with double-inertial effects for nonconvex equilibrium problems

TL;DR

This paper introduces a novel relaxation proximal point algorithm with double inertial effects designed for non-convex equilibrium problems, providing convergence guarantees and numerical validation.

Contribution

It proposes a new algorithm that incorporates double inertial effects for non-convex equilibrium problems, extending existing methods with proven convergence.

Findings

Global convergence of the proposed algorithm is established.

Numerical tests confirm the theoretical convergence results.

The method generalizes some known results as special cases.

Abstract

In this paper, we present a relaxation proximal point method with double inertial effects to approximate a solution of a non-convex equilibrium problem. We give global convergence results of the iterative sequence generated by our algorithm. Some known results are recovered as special cases of our results. Numerical test is given to support the theoretical findings.