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An exact penalty method for semidefinite-box-constrained low-rank matrix optimization problems
Liu, Tianxiang1; Lu, Zhaosong2; Chen, Xiaojun1; Dai, Yu-Hong3
2020
Source PublicationIMA JOURNAL OF NUMERICAL ANALYSIS
ISSN0272-4979
Volume40Issue:1Pages:563-586
AbstractThis paper considers a matrix optimization problem where the objective function is continuously differentiable and the constraints involve a semidefinite-box constraint and a rank constraint. We first replace the rank constraint by adding a non-Lipschitz penalty function in the objective and prove that this penalty problem is exact with respect to the original problem. Next, for the penalty problem we present a nonmonotone proximal gradient (NPG) algorithm whose subproblem can be solved by Newton's method with globally quadratic convergence. We also prove the convergence of the NPG algorithm to a first-order stationary point of the penalty problem. Furthermore, based on the NPG algorithm, we propose an adaptive penalty method (APM) for solving the original problem. Finally, the efficiency of an APM is shown via numerical experiments for the sensor network localization problem and the nearest low-rank correlation matrix problem.
Keywordrank constrained optimization non-Lipschitz penalty nonmonotone proximal gradient penalty method
DOI10.1093/imanum/dry069
Indexed BySCI
Language英语
Funding ProjectAcademy of Mathematics and Systems Science Polytechnic University Joint Research Institute Postdoctoral Scheme ; Natural Sciences and Engineering Research Council ; National Natural Science Foundation of China/Hong Kong Research Grant Council[N-PolyU504/14] ; Chinese Natural Science Foundation[11631013] ; Chinese Natural Science Foundation[11331012] ; National 973 Program of China[2015CB856002]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000544720400018
PublisherOXFORD UNIV PRESS
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/51748
Collection中国科学院数学与系统科学研究院
Corresponding AuthorChen, Xiaojun
Affiliation1.Hong Kong Polytech Univ, Dept Appl Math, Hong Kong, Peoples R China
2.Simon Fraser Univ, Dept Math, Burnaby, BC, Canada
3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China
Recommended Citation
GB/T 7714
Liu, Tianxiang,Lu, Zhaosong,Chen, Xiaojun,et al. An exact penalty method for semidefinite-box-constrained low-rank matrix optimization problems[J]. IMA JOURNAL OF NUMERICAL ANALYSIS,2020,40(1):563-586.
APA Liu, Tianxiang,Lu, Zhaosong,Chen, Xiaojun,&Dai, Yu-Hong.(2020).An exact penalty method for semidefinite-box-constrained low-rank matrix optimization problems.IMA JOURNAL OF NUMERICAL ANALYSIS,40(1),563-586.
MLA Liu, Tianxiang,et al."An exact penalty method for semidefinite-box-constrained low-rank matrix optimization problems".IMA JOURNAL OF NUMERICAL ANALYSIS 40.1(2020):563-586.
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