Exceptional Families and Existence Results for Nonlinear Complementarity Problem

In this paper we establish several sufficient conditions for the existence of a solution to the linear and some classes of nonlinear complementarity problems. These conditions involve a notion of the ``exceptional family of elements' introduced by Smith 19] and Isac, Bulavski and Kalashnikov 4], where the authors have shown that the nonexistence of the ``exceptional family of elements' implies solvability of the complementarity problem. In particular, we establish several sufficient conditions for the nonexistence as well as for the existence of the exceptional family of elements.