(DP 1993-08) On Q-Matrices and the Boundedness of Solutions to Linear Complementarity Problems

Abstract

This paper is concerned with the existence and boundedness of the solutions to the linear complementarity problem w = Mz + q, w ≥ 0, z ≥ 0, wTz = 0, for each q є Rn. It has been previously established that if M is copositive plus, then the solution set is nonempty and bounded for each q є Rn iff M is a Q-matrix. This result is shown to be valid also for L2-matrices, Po-matrices, nonnegative matrices and Z-matrices.