TY - JOUR
T1 - SNIG Property of Matrix Low-Rank Factorization Model
AU - Wang , Hong
AU - Liu , Xin
AU - Chen , Xiaojun
AU - Yuan , Yaxiang
JO - Journal of Computational Mathematics
VL - 3
SP - 374
EP - 390
PY - 2018
DA - 2018/06
SN - 36
DO - http://doi.org/10.4208/jcm.1707-m2016-0796
UR - https://global-sci.org/intro/article_detail/jcm/12266.html
KW - Low rank factorization, Nonconvex optimization, Second-order optimality condition, Global minimizer.
AB - <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>