@Article{JCM-36-3,
author = {Wang, Hong and Xin, Liu and Xiaojun, Chen and Yuan, Yaxiang},
title = {SNIG Property of Matrix Low-Rank Factorization Model},
journal = {Journal of Computational Mathematics},
year = {2018},
volume = {36},
number = {3},
pages = {374--390},
abstract = {<p style="text-align: justify;">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
(&quot;Second-order Necessary optimality Implies Global optimality&quot;) 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.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1707-m2016-0796},
url = {https://global-sci.com/article/84473/snig-property-of-matrix-low-rank-factorization-model}
}