KMS Of Academy of mathematics and systems sciences, CAS
| AN ALTERNATING MINIMIZATION METHOD FOR MATRIX COMPLETION PROBLEMS | |
| Shen, Yuan1; Liu, Xin2 | |
| 2020-06-01 | |
| Source Publication | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
 |
| ISSN | 1937-1632 |
| Volume | 13Issue:6Pages:1757-1772 |
| Abstract | 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. |
| Keyword | Matrix completion symmetric low rank product minimization singular value decomposition alternating minimization |
| DOI | 10.3934/dcdss.2020103 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | 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 Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000526086300010 |
| Publisher | AMER INST MATHEMATICAL SCIENCES-AIMS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/51161 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Liu, Xin |
| Affiliation | 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 |
| 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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