Lipschitz stability for a class of parametric optimization problems with polyhedral feasible set mapping

Abstract This paper is devoted to the Lipschitz analysis of the solution sets and optimal values for a class of parametric optimization problems involving a polyhedral feasible set mapping and a quadratic objective function with parametric linear part. Recall that a multifunction is said to be polyhedral if its graph is the union of finitely many polyhedral convex sets.While this kind of model under a graph-convex polyhedral feasible set mapping F has been well-studied in the literature, we intent to extend these studies to the case of a general polyhedral F . In the general case we show that if the optimal value function is upper semicontinuous,then the optimal set mapping is upper (outer) Lipschitz continuous on its domain, and the optimal value function is Lipschitz continuous on each bounded convex subset of its domain. Moreover, we revisit classical results needed in the proofs and discuss special classes of problems which fit into the model.