A new strategy for solving variational inequalities in bounded polytopes∗

Abstract

We consider variational inequality problems where the convex set under consideration is a bounded polytope. We define an associated box constrained minimization problem and we prove that, under a general condition on the Jacobian, the stationary points of the minimization problems are solutions of the variational inequality problem. The condtion includes the case where the operator is monotone. Based on this result we develop an algorithm that can solve large scale problems. We present numerical experiments.