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Matrix Optimization Over Low-Rank Spectral Sets: Stationary Points and Local and Global Minimizers
Journal of Optimization Theory and Applications ( IF 1.9 ) Pub Date : 2019-12-09 , DOI: 10.1007/s10957-019-01606-8
Xinrong Li , Naihua Xiu , Shenglong Zhou

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.

中文翻译:

低秩谱集上的矩阵优化:静止点和局部和全局最小化器

在本文中,我们考虑以变量为矩阵的矩阵优化,该矩阵被约束为低秩谱集,其中低秩谱集是低秩集和谱集的交集。考虑了三个典型的谱集,产生了三个低秩谱集。对于每个低秩谱集,我们首先计算给定点在该集合上的投影及其法锥的公式,然后在此基础上研究矩阵优化在低秩谱集上的诱导平稳点。最后,我们揭示了每个静止点和每个局部/全局最小化器之间的关系。
更新日期:2019-12-09
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