Optimality Conditions for Rank-Constrained Matrix Optimization

被引：0
|
作者：
Xin-Rong Li
Wen Song
Nai-Hua Xiu
机构：
[1] Beijing Jiaotong University,Department of Applied Mathematics
[2] Harbin Normal University,School of Mathematical Sciences
来源：
Journal of the Operations Research Society of China | 2019年 / 7卷
关键词：
Matrix optimization; Rank constraint; Normal cone; First-order optimality condition; Second-order optimality condition; 90C26; 90C30; 90C46;
D O I：
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中图分类号：
学科分类号：
摘要：
In this paper, we comprehensively study optimality conditions for rank-constrained matrix optimization (RCMO). By calculating the Clarke tangent and normal cones to a rank-constrained set, along with the given Fréchet, Mordukhovich normal cones, we investigate four kinds of stationary points of the RCMO and analyze the relations between each stationary point and local/global minimizer of the RCMO. Furthermore, the second-order optimality condition of the RCMO is achieved with the help of the Clarke tangent cone.
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页码：285 / 301
页数：16
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