Numerical Solution for Pseudomonotone Variational Inequality Problems by Extragradient Methods

Abstract

In this work we analyze from the numerical viewpoint the class of projection methods for solving pseudomonotone variational inequality problems. We focus on some specific extragradient-type methods that do not require differentiability of the operator and we address particular attention to the steplength choice. Subsequently, we analyze the hyperplane projection methods in which we construct an appropriate hyperplane which strictly separates the current iterate from the solutions of the problem. Finally, in order to illustrate the effectiveness of the proposed methods, we report the results of a numerical experimentation.