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
发表期刊	JOURNAL OF COMPUTATIONAL MATHEMATICS
ISSN	0254-9409
卷号	36 期号:3 页码:374-390
摘要	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.
关键词	Low rank factorization Nonconvex optimization Second-order optimality condition Global minimizer
DOI	10.4208/jcm.1707-m2016-0796
语种	英语
资助项目	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研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000455995700004
出版者	GLOBAL SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/32214
专题	计算数学与科学工程计算研究所
通讯作者	Wang, Hong
作者单位	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
推荐引用方式 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.