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Matrix optimisation over low-rank spectral sets: Stationary points, local and global minimizers

Matrix optimisation over low-rank spectral sets: Stationary points, local and global minimizers
Matrix optimisation over low-rank spectral sets: Stationary points, local and global minimizers
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.
Global minimizer, Local minimizer, Low-rank spectral set, Matrix optimization, Stationary point
0022-3239
895-930
Li, XinRong
99a48648-d55a-43e4-8442-0028650cba1b
Xiu, Naihua
8b5770f7-ae35-4dbe-884a-02fb4ea27bee
Zhou, Shenglong
d183edc9-a9f6-4b07-a140-a82213dbd8c3
Li, XinRong
99a48648-d55a-43e4-8442-0028650cba1b
Xiu, Naihua
8b5770f7-ae35-4dbe-884a-02fb4ea27bee
Zhou, Shenglong
d183edc9-a9f6-4b07-a140-a82213dbd8c3

Li, XinRong, Xiu, Naihua and Zhou, Shenglong (2020) Matrix optimisation over low-rank spectral sets: Stationary points, local and global minimizers. Journal of Optimization Theory and Applications, 184 (3), 895-930. (doi:10.1007/s10957-019-01606-8).

Record type: Article

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.

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Submitted date: 2018
Accepted/In Press date: 23 October 2019
e-pub ahead of print date: 9 December 2019
Published date: 1 March 2020
Additional Information: Funding Information: This work was supported in part by the National Natural Science Foundation of China (11431002). Publisher Copyright: © 2019, Springer Science+Business Media, LLC, part of Springer Nature.
Keywords: Global minimizer, Local minimizer, Low-rank spectral set, Matrix optimization, Stationary point

Identifiers

Local EPrints ID: 437104
URI: http://eprints.soton.ac.uk/id/eprint/437104
ISSN: 0022-3239
PURE UUID: 312da87c-151e-4b76-a962-27d25b33fd4f
ORCID for Shenglong Zhou: ORCID iD orcid.org/0000-0003-2843-1614

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Date deposited: 17 Jan 2020 17:31
Last modified: 16 Mar 2024 08:05

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Contributors

Author: XinRong Li
Author: Naihua Xiu
Author: Shenglong Zhou ORCID iD

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