The stability of a generalized variational inequality problem with the nuclear norm function

Abstract

This paper is to study the stability of the generalized variational inequality (GVI) problem whose convex function is the nuclear norm of a linear matrix mapping. The strict Robinson constraint qualification and the second-order sufficient optimality conditions for the GVI problem are proposedand are demonstrated as sufficient conditions for the isolated calmness of the inverse of the KKT (Karush-Kuhn-Tucker) mapping. The constraint non-degeneracy condition and the strong second-order sufficient optimality conditions for the GVI problem are proposed and are proven to be sufficient conditions for the strong regularity of the KKT system.