The Generalized Horizontal Linear Complementarity Problem

Let $M,~N in R^{m imes n}, m geq n,$ 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.