A modified self-adaptive extragradient method for pseudomonotone equilibrium problem in a real Hilbert space with applications

Abstract

In this paper, we consider an improvement of the extragradient method to figure out the numerical solution for pseudomonotone equilibrium problems in arbitrary real Hilbert space. A new method is proposed with an inertial scheme and a self adaptive step size rule that is revised on each iteration based on the previous three iterations. The weak convergence of the method is proved by assuming standard cost bifunction assumptions. We also consider the application of our results to solve different kinds of variational inequality problems and a particular class of fixed point problems. For a numerical part, we study the well-known Nash-Cournot equilibrium model and other test problems to support our well-established convergence results and to ensure that our proposed method has a competitive edge over CPU time and a number of iterations.