An Interior Proximal Method for Solving Monotone Generalized Variational Inequalities

Abstract

We present a new method for solving generalized variational inequalities on polyhedra. The method is based on an interior-quadratic term which replaces the usual quadratic term. This leads to an interior proximal type algorithm. We first solve a monotone generalized variational inequalities satisfying a certain Lipschitz condition. Next, we combine this technique with line search technique to obtain a convergent algorithm for monotone generalized variational inequalities without Lipschitz condition. Finally some preliminary computational results are given.