Existence theory and Q-matrix characterization for the generalized linear complementarity problem Original Research Article

Necessary and sufficient conditions for existence of solutions and a characterization of the set of Q-matrices for the generalized linear complementarity problem (GLCP) are presented. The results lead to an algorithm for solving the GLCP for any general vertical block matrix and provide an insight into the geometry of the problem. It is also shown that the GLCP is NP-complete in the case of a general vertical block matrix.