SNIG PROPERTY OF MATRIX LOW-RANK FACTORIZATION MODEL

doi:10.4208/jcm.1707-m2016-0796

	SNIG PROPERTY OF MATRIX LOW-RANK FACTORIZATION MODEL
	Wang, Hong 1; Liu, Xin2 ; Chen, Xiaojun 1; Yuan, Ya-xiang2
	2018
Source Publication	JOURNAL OF COMPUTATIONAL MATHEMATICS
ISSN	0254-9409
Volume	36 Issue:3 Pages: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 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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