Sensitivity analysis for variational inequalities

This paper studies 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, it shows that the perturbed local solution set is Lipschitz continuous and directionally differentiable. Even when the directional differentiability is not guaranteed, the paper is still able to describe and characterize first-order information concerning the perturbed local solution set. It also discusses relations to nonlinear programming sensitivity analysis.