Generalizations of R0 and SSM properties; Extended Horizontal Linear Complementarity Problem

TL;DR

This paper introduces generalized matrix properties R0-W and SSM-W, proves existence and uniqueness results for extended horizontal linear complementarity problems, and characterizes the connectedness of their solution sets.

Contribution

It extends classical matrix properties to broader classes and establishes new existence, uniqueness, and topological results for related complementarity problems.

Findings

Existence results for matrices with R0-W and SSM-W properties.

Equivalence of SSM-W property and unique solutions under certain conditions.

Necessary and sufficient conditions for solution set connectedness.

Abstract

In this paper, we first introduce R0-W and SSM-W properties for the set of matrices which is a generalization of R0 and the strictly semimonotone matrix. We then prove some existence results for the extended horizontal linear complementarity problem when the involved matrices have these properties. With an additional condition on the set of matrices, we prove that the SSM-W property is equivalent to the unique solution for the corresponding extended horizontal linear complementarity problems. Finally, we give a necessary and sufficient condition for the connectedness of the solution set of the extended horizontal linear complementarity problems.