CSpace  > 计算数学与科学工程计算研究所
Wang Hong1; Liu Xin2; Chen Xiaojun1; Yuan Yaxiang2
Source Publicationjournalofcomputationalmathematics
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.
Funding Project[NSFC] ; [China 863 Program] ; [National Center for Mathematics and Interdisciplinary Sciences, CAS] ; [NSFC/Hong Kong Research Grant Council]
Document Type期刊论文
Recommended Citation
GB/T 7714
Wang Hong,Liu Xin,Chen Xiaojun,et al. snigpropertyofmatrixlowrankfactorizationmodel[J]. journalofcomputationalmathematics,2018,36(3):374.
APA Wang Hong,Liu Xin,Chen Xiaojun,&Yuan Yaxiang.(2018).snigpropertyofmatrixlowrankfactorizationmodel.journalofcomputationalmathematics,36(3),374.
MLA Wang Hong,et al."snigpropertyofmatrixlowrankfactorizationmodel".journalofcomputationalmathematics 36.3(2018):374.
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