Proximal method for solving nonmonotone variational inequalities

Abstract

A generalized variational inequality is considered. In addition to ordinary inequalities, it contains a quasivariational inequality and an implicit complementarity problem. The specific feature of the problem under consideration is that basic mappings inherent in the problem are not monotonic. A proximal method for solving this problem, which guarantees convergence to the solution under rather general assumptions, is suggested. Copyright © 2004 by MAIK "Nauka/Interperiodica".