Perturbed solutions of variational inequality problems over polyhedral sets (Q1089902)

This paper is concerned with variational inequality problems defined over polyhedral sets, which provide a generalization of many diverse problems of mathematical programming, complementarity, and mathematical economics. Differentiability properties of locally unique perturbed solutions to such problems are studied. It is shown that, if a simple sufficient condition is satisfied, then the perturbed solution is locally unique, continuous, and directionally differentiable. Furthermore, under an additional regularity assumption, the perturbed solution is also continuously differentiable.