On Cone Orderings and the Linear Complementarity Problem.

摘要

This paper first generalizes a characterization of polyhedral sets having least elements,which is obtained by Cottle and Veinott,to the situation where Euclidean space is partially ordered by some general cone ordering (rather than the usual ordering). We then use this generalization to establish the following characterization of the class C of matrices (C arises as a generalization of the class of Z-matrices, M is a member of C if and only if for every vector q for which the linear complementarity problem (q,M) is feasible,the problem (q,M) has a solution which is the least element of the feasible set.