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

作　　者：赵亚莉 张语乐 张立卫[2] Yali Zhao;Yule Zhang;Liwei Zhang

机构地区：[1]渤海大学数学科学学院,锦州121013 [2]大连理工大学数学科学学院运筹学与控制论研究所,大连116024

出　　处：《中国科学：数学》2022年第1期85-104,共20页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11371070,11971089和11731013);辽宁省教育厅项目(批准号:LJ2019011);辽宁省自然科学基金计划指导项目(批准号:2019-ZD-0502)资助项目。

摘　　要：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.

关 键 词：广义变分不等式 核矩阵范数 稳定性 孤立平稳性 强正则性 严格Robinson约束规范 

分 类 号：O224[理学—运筹学与控制论]