Sensitivity Analysis for Variational Inequalities

In this paper we study the behavior of the local solutions of perturbed variational inequalities, governed by perturbations to both the variational inequality function and the feasible region. Assuming appropriate second-order and regularity conditions, we show that the perturbed local solution set is Lipschitz continuous and directionally differentiable. Even when the directional differentiability is not guaranteed, we are still able to describe and characterize first-order information concerning the perturbed local solution set. We also discuss relations to nonlinear programming sensitivity analysis.