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.
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