Lipschitz continuity of solutions of variational inequalities with a parametric polyhedral constraint

It is proved that the metric projection from a point onto a moving polyhedron is Lipschitz continuous with respect to the perturbations on the right-hand sides of the linear inequalities defining the polyhedron. The property leads to a simple sufficient condition for Lipschitz continuity of a locally unique solution of parametric variational inequalities with a moving polyhedral constraint set. Applications of these results to traffic network equilibrium problems are given in detail.