An exact penalty method for semidefinite-box-constrained low-rank matrix optimization problems

doi:10.1093/imanum/dry069

	An exact penalty method for semidefinite-box-constrained low-rank matrix optimization problems
	Liu, Tianxiang 1; Lu, Zhaosong 3; Chen, Xiaojun 1; Dai, Yu-Hong 2
刊名	IMA JOURNAL OF NUMERICAL ANALYSIS
	2020
卷号	40 期号:1 页码:563-586
关键词	rank constrained optimization non-Lipschitz penalty nonmonotone proximal gradient penalty method
ISSN号	0272-4979
DOI	10.1093/imanum/dry069
英文摘要	This 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.
资助项目	Academy 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研究方向	Mathematics
语种	英语
出版者	OXFORD UNIV PRESS
WOS记录号	WOS:000544720400018
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/51747]
专题	中国科学院数学与系统科学研究院
通讯作者	Chen, Xiaojun
作者单位	1.Hong Kong Polytech Univ, Dept Appl Math, Hong Kong, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China 3.Simon Fraser Univ, Dept Math, Burnaby, BC, Canada
推荐引用方式 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.