核范数函数的广义变分不等式问题的稳定性

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

本文主要研究凸函数为线性矩阵映射核范数的广义变分不等式(generalized variational inequality,GVI)问题的稳定性,提出GVI问题的严格Robinson约束规范和二阶充分最优性条件,并证明它们是KKT(Karush-Kuhn-Tucker)映射逆映射孤立平稳性的充分条件;还给出GVI问题的约束非退化条件和强二阶充分最优性条件,并证明它们是KKT系统强正则性的充分条件.

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 proposed and 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.