Solving Equilibrium Problem with New Inertial Technique

TL;DR

This paper introduces a novel inertial subgradient extragradient method with correction terms for equilibrium problems, demonstrating convergence and improved performance through numerical examples.

Contribution

It presents a new inertial extragradient algorithm with correction terms for equilibrium problems, achieving convergence and enhanced efficiency over existing methods.

Findings

Sequence converges weakly under pseudomonotonicity and Lipschitz conditions.

Linear convergence rate established for strongly pseudomonotone bifunctions.

Numerical examples show significant improvement over existing methods.

Abstract

We propose in this work a subgradient extragradient method with inertial and correction terms for solving equilibrium problems in a real Hilbert space. We obtain that the sequence generated by our proposed method converges weakly to a point in the solutions set of the equilibrium problem when the associated bivariate function is pseudomonotone and satisfies Lipschitz conditions. Furthermore, in a case where the bifunction is strongly pseudomonotone, we establish a linear convergence rate. Lastly, through different numerical examples, we demonstrate that the incorporation of multiple correction terms significantly improves our proposed method when compared with other methods in the literature.