New inertial regularized algorithm for solving strongly pseudomonotone equilibrium problems

TL;DR

This paper presents a novel inertial regularized algorithm for strongly pseudomonotone equilibrium problems that converges strongly without prior knowledge of problem constants and demonstrates linear convergence when these are known.

Contribution

The paper introduces a new algorithm combining proximal regularization and inertial effects that does not require prior knowledge of problem constants, with proven convergence properties.

Findings

The algorithm converges strongly without prior knowledge of constants.

Linear convergence rate is established when problem constants are known.

Numerical experiments confirm the effectiveness and compare favorably with existing methods.

Abstract

The article introduces a new algorithm for solving a class ofequilibrium problems involving strongly pseudomonotone bifunctions with Lipschitz-type condition. We describe how to incorporate the proximal-like regularized technique with inertial effects. The main novelty of the algorithm is that it can be done without previously knowing the information on the strongly pseudomonotone and Lipschitz-type constants of cost bifunction. A reasonable explain for this is that the algorithm uses a sequence of stepsizes which is diminishing and non-summable. Theorem of strong convergence is proved. In the case, when the information on the modulus of strong pseudomonotonicity and Lispchitz-type constant is known,the rate of linear convergence of the algorithm has been established. Several of numerical experiments are performed to illustrate the convergence of the algorithm and also compare it with other algorithms.