Sensitivity Analysis of Parameterized Variational Inequalities

We discuss in this paper local uniqueness, continuity and differentiability properties of solutions of parameterized variational inequalities (generalized equations). To this end we use two types of techniques. One approach consists in formulating variational inequalities in a form of optimization problems, based on regularized gap functions, and applying a general theory of perturbation analysis of parameterized optimization problems. Another approach is based on a theory of contingent (outer graphical) derivatives and some results about differentiability properties of metric projections.