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AN ALTERNATING MINIMIZATION METHOD FOR MATRIX COMPLETION PROBLEMS
Shen, Yuan1; Liu, Xin2
2020-06-01
Source PublicationDISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
ISSN1937-1632
Volume13Issue:6Pages:1757-1772
AbstractMatrix 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.
KeywordMatrix completion symmetric low rank product minimization singular value decomposition alternating minimization
DOI10.3934/dcdss.2020103
Indexed BySCI
Language英语
Funding ProjectNSFC[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 Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000526086300010
PublisherAMER INST MATHEMATICAL SCIENCES-AIMS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/51161
Collection中国科学院数学与系统科学研究院
Corresponding AuthorLiu, Xin
Affiliation1.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
Recommended Citation
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.
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