On the Lipschitz behavior of optimal solutions in parametric problems of quadratic optimization and linear complementarity

We consider parametric optimization problems of the type min where Г is a polyhedral multifunction. It is shown that, under natural assumptions, the optimal set mapping and the infimum function of such a problem are Lipschitzian in some sense. The results are applied to a (generally non-convex) quadratic optimization problem parameterized in the linear part of the objective function and in the right-hand side of the constraints. In out studies we essentially use arguments from linear parametric optimization and S.M. Robinson's theorem on the upper Lipschitz continuity of polyhedral multifunctions.