Complementary irreducibilityS– matrices with connections to solutions of the linear complementarity problem
Abdelaziz Foul · Optimization · 1996
A matrix Y is said to be complementary irreducibly S if it is an S–matrix and whenever , then r+s>0. Here r, SϵRn and Y is an n×2n matrix. For a given complementary irreducibly S–Matrix Yand an arbitrary nonnegative vector b of R n, we prove that the set admits a greatest element. As a consequence, we extend some results by Cottle and Pang on the existence of solutions to the linear complementarity problem that can be generated from least elements of polyhedral sets.