Generalized Linear Complementarity Problems

Abstract

We introduce the concept of the generalized (monotone) linear complementarity problem (GLCP) in order to unify LP, convex QP, monotone LCP, and mixed monotone LCP. We establish the basic properties of GLCP and develop canonical forms for its representation. We show that the GLCP reduces to a monotone LCP in the same variables. This implies that many results which hold true for monotone LCP extend to GLCP. In particular, any interior point algorithm for monotone LCP extends to an interior point algorithm for GLCP.