Sensitivity of solutions to variational inequalities on Banach spaces

We analyze the sensitivity of parameterized variational inequalities for co nvex polyhedric sets in reflexive Banach spaces. We compute a generalized d erivative of the solution mapping where the formula for the derivative is g iven in terms of the solutions to an auxiliary variational inequality. Thes e results are distinguished from other work in this area by the fact that t hey do not depend on the uniqueness of the solutions to the variational ine qualities. To obtain our results, we use second-order epi-derivatives to an alyze the second-order properties of polyhedric sets. We apply our results to sensitivity analyses of stationary points and KKT pairs associated with constrained infinite-dimensional optimization problems.