Nonlinear Perturbations of Polyhedral Normal Cone Mappings and Affine Variational Inequalities

Abstract

This paper establishes an upper estimate for the Frechet normal cone to the graph of the nonlinearly perturbed polyhedral normal cone mappings in finite dimensional spaces. Under a positive linear independence assumption on the normal vectors of the active constraints at the point in question, the result leads to an upper estimate for values of the Mordukhovich coderivative of such mappings. On the basis, new results on solution stability of parametric affine variational inequalities under nonlinear perturbations are derived.