Year: 2018
Author: Hong Wang, Xin Liu, Xiaojun Chen, Yaxiang Yuan
Journal of Computational Mathematics, Vol. 36 (2018), Iss. 3 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1707-m2016-0796
Journal of Computational Mathematics, Vol. 36 (2018), Iss. 3 : pp. 374–390
Published online: 2018-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Low rank factorization Nonconvex optimization Second-order optimality condition Global minimizer.