Conditions ensuring the applicability of cutting-plane methods for solving variational inequalities

Let VIP(F, C) denote the variational inequality problem associated with the mapping F and the closed convex set C. In this paper we introduce weak conditions on the mapping F that allow the development of a convergent cutting-plane framework for solving VIP(F, C). In the process we introduce, in a natural way, new and useful notions of generalized monotonicity for which first order characterizations are presented.