A new inertial condition on the subgradient extragradient method for solving pseudomonotone equilibrium problem

Abstract

In this paper, we study the pseudomonotone equilibrium problem. We consider a new inertial condition for the subgradient extragradient method with self-adaptive step size for approximating a solution of the equilibrium problem in a real Hilbert space. Our proposed method contains inertial factor with new conditions that only depend on the iteration coefficient. We obtain a weak convergence result of the proposed method under weaker conditions on the inertial factor than many existing conditions in the literature. Finally, we present some numerical experiments for our proposed method and compared it to existing methods in the literature. Our result improves, extends, and generalizes several existing results in the literature.