Exceptional families and finite-dimensional variational inequalities over polyhedral convex sets

摘要

A new concept of exceptional family for nonlinear variational inequalities over polyhedral sets is introduced in this paper. It generalizes the concepts for complementarity problem introduced by Smith and Isac. We applied the new analytical tool to the study of existence problem for variational inequalities. It is shown that our existence condition is weaker than most of the sufficient conditions which have been known.