Sufficient matrices and the linear complementarity problem (Q1121805)

A new class of matrices, related to the linear complementarity problem (LCP), the so called ``row sufficient'' matrices, are introduced. Respectively, the transpose of such a matrix is called ``column sufficient''. Two important results are proved: (i) A matrix \(M\) is row sufficient iff for every \(q\in \mathbb R^n\) any Kuhn-Tucker-point of the associated quadratic program solves the LCP \((q,M)\); (ii) \(M\) is column sufficient iff for every \(q\in \mathbb R^n\) the LCP \((q,M)\) has a convex solution set. The connections with other well-known matrix classes in linear complementarity theory are also discussed.