Modified Explicit Self-Adaptive Two-Step Extragradient Method for Equilibrium Programming in a Real Hilbert Space

Nattawut Pholasa, Nuttapol Pakkaranang, Habib ur Rehman, Thanatporn Bantaojai, Muhammad Jabir Khan, Wuttikorn Chaloemwiriya

Abstract

The primary objective of this study is to present a new self-adaptive method to solve an equilibrium problem involving pseudomonotone bifunction in real Hilbert spaces. This method could be viewed as an improvement of the paper title Extragradient algorithms extended to equilibrium problem by Tran et al. [D.Q. Tran, M.L. Dung, V.H. Nguyen,  Extragradient algorithms extended to equilibrium problems, Optim. 57 (2008) 749--776]. A weak convergence theorem for the generated sequence has been proven and implemented to solve variational inequality problems. We have used different numerical examples to illustrate our well-established convergence results.