A Regularization Approach for Variational Inequalities with Pseudo-Monotone Operators

Abstract

This paper is motivated by the observation that the classical regularization method is not efficient enough to regularize variational inequalities with noncoercive pseudo-monotone operators. The main reason for its deficiency is the fact that any perturbation of pseudo-monotone operators may not be pseudo-monotone. In this contribution we study the variational inequalities with non-coercive pseudo-monotone operators. Instead of the classical regularization method to regularize the problem we use a different approach which is based on the theory of linear compact operators.