Matrix Optimization Over Low-Rank Spectral Sets: Stationary Points and Local and Global Minimizers

被引:0
作者
Xinrong Li
Naihua Xiu
Shenglong Zhou
机构
[1] Beijing Jiaotong University,Department of Applied Mathematics
[2] University of Southampton,School of Mathematics
来源
Journal of Optimization Theory and Applications | 2020年 / 184卷
关键词
Matrix optimization; Low-rank spectral set; Stationary point; Local minimizer; Global minimizer; 90C26; 90C30; 90C46;
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学科分类号
摘要
In this paper, we consider matrix optimization with the variable as a matrix that is constrained into a low-rank spectral set, where the low-rank spectral set is the intersection of a low-rank set and a spectral set. Three typical spectral sets are considered, yielding three low-rank spectral sets. For each low-rank spectral set, we first calculate the projection of a given point onto this set and the formula of its normal cone, based on which the induced stationary points of matrix optimization over low-rank spectral sets are then investigated. Finally, we reveal the relationship between each stationary point and each local/global minimizer.
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页码:895 / 930
页数:35
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