The Generalized Linear Complementarity Problem: Least Element Theory and Z-Matrices

Existence of solutions to the Generalized Linear Complementarity Problem (GLCP) is characterized when the associated matrix is a vertical blockZ-matrix. It is shown that if solutions exist, then one must be the leastelement of the feasible region. Moreover, the vertical block Z-matrixbelongs to the class of matrices where feasibility implies existence of asolution to the GLCP. The concept of sufficient matrices of class Z isinvestigated to obtain additional properties of the solution set.