SNIG PROPERTY OF MATRIX LOW-RANK FACTORIZATION MODEL
文献类型：期刊论文
| 作者 | Wang, Hong1; Liu, Xin2 ; Chen, Xiaojun1; Yuan, Ya-xiang2
|
| 刊名 | JOURNAL OF COMPUTATIONAL MATHEMATICS
 |
| 出版日期 | 2018 |
| 卷号 | 36期号:3页码:374-390 |
| 关键词 | Low rank factorization Nonconvex optimization Second-order optimality condition Global minimizer |
| ISSN号 | 0254-9409 |
| DOI | 10.4208/jcm.1707-m2016-0796 |
| 英文摘要 | 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. |
| 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 |
| 语种 | 英语 |
| WOS记录号 | WOS:000455995700004 |
| 出版者 | GLOBAL SCIENCE PRESS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/32213]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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