Snig property of matrix low-rank factorization model*

Hong Wang, Xin Liu, Xiaojun Chen, Ya xiang Yuan

Research output: Journal article publicationJournal articleAcademic researchpeer-review


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.

Original languageEnglish
Pages (from-to)374-390
Number of pages17
JournalJournal of Computational Mathematics
Issue number3
Publication statusPublished - 28 Mar 2018


  • Global minimizer
  • Low rank factorization
  • Nonconvex optimization
  • Second-order optimality condition

ASJC Scopus subject areas

  • Computational Mathematics

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