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SNIG PROPERTY OF MATRIX LOW-RANK FACTORIZATION MODEL
Wang, Hong1; Liu, Xin2; Chen, Xiaojun1; Yuan, Ya-xiang2
2018
Source PublicationJOURNAL OF COMPUTATIONAL MATHEMATICS
ISSN0254-9409
Volume36Issue:3Pages:374-390
AbstractRecently, 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.
KeywordLow rank factorization Nonconvex optimization Second-order optimality condition Global minimizer
DOI10.4208/jcm.1707-m2016-0796
Language英语
Funding ProjectNSFC[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 AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000455995700004
PublisherGLOBAL SCIENCE PRESS
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/32214
Collection计算数学与科学工程计算研究所
Affiliation1.Hong Kong Polytech Univ, Dept Appl Math, Hong Kong, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Sci & Engn Comp, Beijing, Peoples R China
Recommended Citation
GB/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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