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

Xinrong Li (), Naihua Xiu () and Shenglong Zhou ()
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Xinrong Li: Beijing Jiaotong University
Naihua Xiu: Beijing Jiaotong University
Shenglong Zhou: University of Southampton

Journal of Optimization Theory and Applications, 2020, vol. 184, issue 3, No 10, 895-930

Abstract: Abstract 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.

Keywords: Matrix optimization; Low-rank spectral set; Stationary point; Local minimizer; Global minimizer; 90C26; 90C30; 90C46 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-019-01606-8

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