A class of singular Ro-matrices and extensions to semidefinite linear complementarity problems

Abstract

For ARnxn and qRn, the linear complementarity problem LCP(A, q) is to determine if there is xRn such that x ≥ 0; y = Ax + q ≥ 0 and xT y = 0. Such an x is called a solution of LCP(A,q). A is called an Ro-matrix if LCP(A,0) has zero as the only solution. In this article, the class of R0-matrices is extended to include typically singular matrices, by requiring in addition that the solution x above belongs to a subspace of Rn. This idea is then extended to semidefinite linear complementarity problems, where a characterization is presented for the multplicative transformation.

Keywords

• Ro-matrix
• semidefinite linear complementarity problems
• Moore-Penroseinverse
• group inverse