Strong Convergence of a Parallel Extragradient-Like Algorithm Involving Pseudo-Monotone Mappings for Solving Common Variational Inequality Problems

Suparat Kesornprom, Prasit Cholamjiak, Watcharaporn Cholamjiak

Abstract

The purpose of this paper is to introduce a new parallel extragradient-like algorithm for solving common variational inequality problems with pseudo-monotone and Lipschitz continuous map- pings in a Hilbert space. The iterative algorithm combines inertial ideas and hybrid extragradient ideas with the Armijo-like step size rule. Strong convergence of the algorithm is obtained under some suitable conditions.