(DP 1994-04) A Note on Isotone Solutions of the Parametric Linear Complementarity Problem

Abstract

This paper shows that the parametric linear complementarity problem w = Mz + q + αp, w ≥ 0, z ≥ 0, wTz = 0, α ≥ 0 has isotone complementary solutions for q = 0 and every p iff M is a P-matrix. Thus, isotonicity for every q ≥ 0 and every p reduces to monotonicity where M is a P-matrix. By excluding q = 0, it is shown that isotonicity is possible for every 0 ¡Ù q ≥ 0 and every p where M is not P-matrix.