AN ALTERNATING MINIMIZATION METHOD FOR MATRIX COMPLETION PROBLEMS

doi:10.3934/dcdss.2020103

	AN ALTERNATING MINIMIZATION METHOD FOR MATRIX COMPLETION PROBLEMS
	Shen, Yuan 1; Liu, Xin 2
刊名	DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
	2020-06-01
卷号	13 期号:6 页码:1757-1772
关键词	Matrix completion symmetric low rank product minimization singular value decomposition alternating minimization
ISSN号	1937-1632
DOI	10.3934/dcdss.2020103
英文摘要	Matrix completion problems have applications in various domains such as information theory, statistics, engineering, etc. Meanwhile, solving matrix completion problems is not a easy task since the nonconvex and nonsmooth rank operation is involved. Existing approaches can be categorized into two classes. The first ones use nuclear norm to take the place of rank operation, and any convex optimization algorithms can be used to solve the reformulated problem. The limitation of this class of approaches is singular value decomposition (SVD) is involved to tackle the nuclear norm which significantly increases the computational cost. The other ones factorize the target matrix by two slim matrices. Fast algorithms for solving the reformulated nonconvex optimization problem usually lack of global convergence, meanwhile convergence guaranteed algorithms require restricted stepsize. In this paper, we consider the matrix factorization model for matrix completion problems, and propose an alternating minimization method for solving it. The global convergence to a stationary point or local minimizer is guaranteed under mild conditions. We compare the proposed algorithm with some state-of-the-art algorithms in solving a bunch of testing problems. The numerical results illustrate the efficiency and great potential of our algorithm.
资助项目	NSFC[11401295] ; NSFC[11726618] ; NSFC[11622112] ; NSFC[11471325] ; NSFC[91530204] ; NSFC[11688101] ; Major Program of the National Social Science Foundation of China[12ZD114] ; National Social Science Foundation of China[15BGL158] ; National Social Science Foundation of China[17BTQ063] ; Qinglan Project of Jiangsu Province ; Social Science Foundation of Jiangsu Province[18GLA002] ; National Center for Mathematics and Interdisciplinary Sciences, CAS ; Key Research Program of Frontier Sciences, CAS[QYZDJ-SSW-SYS010]
WOS研究方向	Mathematics
语种	英语
出版者	AMER INST MATHEMATICAL SCIENCES-AIMS
WOS记录号	WOS:000526086300010
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/51160]
专题	中国科学院数学与系统科学研究院
通讯作者	Liu, Xin
作者单位	1.Nanjing Univ Finance & Econ, Sch Appl Math, Nanjing, Peoples R China 2.Chinese Acad Sci, Univ Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Sci & Engn Comp, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Shen, Yuan,Liu, Xin. AN ALTERNATING MINIMIZATION METHOD FOR MATRIX COMPLETION PROBLEMS[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S,2020,13(6):1757-1772.
APA	Shen, Yuan,&Liu, Xin.(2020).AN ALTERNATING MINIMIZATION METHOD FOR MATRIX COMPLETION PROBLEMS.DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S,13(6),1757-1772.
MLA	Shen, Yuan,et al."AN ALTERNATING MINIMIZATION METHOD FOR MATRIX COMPLETION PROBLEMS".DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S 13.6(2020):1757-1772.