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核范数函数的广义变分不等式问题的稳定性

Yali Zhao,Yule Zhang,Liwei Zhang

Science in China(Series A)（2022）

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Abstract
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 inequal-ity,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.
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