GENERALIZED LINEAR COMPLEMENTARITY-PROBLEMS

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 we show, under suitable conditions, that feasibility of a generalized linear complementarity problem (i.e., defined over a more general closed convex cone in a real Hilbert space) implies solvability whenever the operator is copositive plus on that cone. We 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. We also prove a perturbation result for generalized linear complementarity problems. © 1990 North-Holland.