The Generalized Horizontal Linear Complementarity Problem

Abstract

Let $M,~N \in R^{m \times n}, m \geq n,$ be vertical block matrices and $\mathbf{q} \in R^{m}.$ We consider the generalized horizontal linear complementarity problem (GHLCP) associated with the pair $\{M,N\}$. Existence and uniqueness of solutions are characterized when the pair $\{M, N\}$ satisfies new generalized column $W$- and column $W_0$-properties.