It has been shown by Lemke that if a matrix is copositive plus on ℝn, then feasibility of the corresponding linear complementarity problem implies solvability. In this article the authors show, under suitable conditions, that feasibility of a generalized linear complementarity problem (i.e., defined over a more general closed convex cone is a real Hilbert space) implies solvability whenever the operator is copositive plus on that cone. They show that among all closed convex cones in a finite dimensional real Hilbert Space, polyhedral cones are the only ones with the property that every copositive plus, feasible GLCP is solvable. The authors also prove a perturbation result for generalized linear complementarity problems.
