Lineality Removal for Copositive-Plus Normal Maps

Abstract

We are concerned with solving affine variational inequalities defined by a linear map A and a polyhedral set C. Most of the existing pivotal methods for such inequalities or mixed linear complementarity problems depend on the existence of extreme points in C or a certain non-singularity property of A with respect to the lineality of C. In this paper, we prove that if A is copositive-plus with respect to the recession cone of C, then the lineality space can be removed without any further assumptions. The reductions given here extend the currently known pivotal methods to solve affine variational inequalities or prove that no solution exists, whenever A is copositive-plus withe respect to the recession cone of C.