EP Theorem for Dual Linear Complementarity Problems

The linear complementarity problem (LCP) belongs to the class of -hard problems. Therefore, we cannot expect a polynomial time solution method for LCPs without requiring some special property of the matrix of the problem. We show that the dual LCP can be solved in polynomial time if the matrix is row sufficient; moreover, in this case, all feasible solutions are complementary. Furthermore, we present an existentially polytime (EP) theorem for the dual LCP with arbitrary matrix. The research of Tibor Illés and Marianna Nagy has been supported by the Hungarian National Research Fund OTKA T 049789 and by the Hungarian Science and Technology Foundation TéT SLO-4/2005. Tamàs Terlaky has been supported by an NSERC Discovery grant, MITACS and the Canada Research Chair program.