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 SNIG PROPERTY OF MATRIX LOW-RANK FACTORIZATION MODEL Wang, Hong1; Liu, Xin2; Chen, Xiaojun1; Yuan, Ya-xiang2 2018 Source Publication JOURNAL OF COMPUTATIONAL MATHEMATICS ISSN 0254-9409 Volume 36Issue:3Pages:374-390 Abstract Recently, the matrix factorization model attracts increasing attentions in handling large-scale rank minimization problems, which is essentially a nonconvex minimization problem. Specifically, it is a quadratic least squares problem and consequently a quartic polynomial optimization problem. In this paper, we introduce a concept of the SNIG ("Second-order Necessary optimality Implies Global optimality") condition which stands for the property that any second-order stationary point of the matrix factorization model must be a global minimizer. Some scenarios under which the SNIG condition holds are presented. Furthermore, we illustrate by an example when the SNIG condition may fail. Keyword Low rank factorization Nonconvex optimization Second-order optimality condition Global minimizer DOI 10.4208/jcm.1707-m2016-0796 Language 英语 Funding Project NSFC[11331012] ; NSFC[11461161005] ; China 863 Program[2013AA122902] ; National Center for Mathematics and Interdisciplinary Sciences, CAS ; NSFC/Hong Kong Research Grant Council[N-PolyU504/14] WOS Research Area Mathematics WOS Subject Mathematics, Applied ; Mathematics WOS ID WOS:000455995700004 Publisher GLOBAL SCIENCE PRESS Citation statistics Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/32214 Collection 计算数学与科学工程计算研究所 Corresponding Author Wang, Hong Affiliation 1.Hong Kong Polytech Univ, Dept Appl Math, Hong Kong, Peoples R China2.Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Sci & Engn Comp, Beijing, Peoples R China Recommended CitationGB/T 7714 Wang, Hong,Liu, Xin,Chen, Xiaojun,et al. SNIG PROPERTY OF MATRIX LOW-RANK FACTORIZATION MODEL[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS,2018,36(3):374-390. APA Wang, Hong,Liu, Xin,Chen, Xiaojun,&Yuan, Ya-xiang.(2018).SNIG PROPERTY OF MATRIX LOW-RANK FACTORIZATION MODEL.JOURNAL OF COMPUTATIONAL MATHEMATICS,36(3),374-390. MLA Wang, Hong,et al."SNIG PROPERTY OF MATRIX LOW-RANK FACTORIZATION MODEL".JOURNAL OF COMPUTATIONAL MATHEMATICS 36.3(2018):374-390.
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