A Partial Characterization of a Class of Matrices Defined by Solutions to the Linear Complementarity Problem

In this paper we analyze the class of matrices, Q 0 , characterized as all n × n matrices, M , for which the linear complementarity problem, w = Mz + q , w , z (ge) 0, w ' z = 0, has a solution whenever q is feasible. The method is to analyze the faces of the linear cone. Cone[ I , - M ] where I is the n × n identity. Essentially, a labelling requirement for the faces is shown necessary for M to be in Q 0 . With proper restrictions and nondegenerate assumptions sufficiency is also shown. These results arc related to the signs of the minors of M and some conjectures in this area are also discussed.

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