Variational Inequalities over Perturbed Polyhedral Convex Sets

This paper provides conditions for existence of a locally unique, Lipschitzian solution of a linear variational inequality posed over a polyhedral convex set in ℝn under perturbation of either or both of the constant term in the variational inequality and the right–hand side of the system of linear constraints defining its feasible set. Conditions for perturbation of just the constant term are well known. Here we show that a suitable extension of those conditions suffices for the more general case in which the right–hand side of the constraints varies also. As a consequence, we obtain existence, uniqueness, and Lipschitz continuity properties of solutions of nonlinear variational inequalities posed over perturbed polyhedral convex sets.