SNIG Property of Matrix Low-Rank Factorization Model (Journal of Computational Mathematics, 2018)
Recently, the matrix factorization model attracts increasing attentions in handlinglarge-scale rank minimization problems, which is essentially a nonconvex minimizationproblem. Specifically, it is a quadratic least squares problem and consequently a quarticpolynomial optimization problem. In this paper, we introduce a concept of the SNIG("Second-order Necessary optimality Implies Global optimality") condition which standsfor the property that any second-order stationary point of the matrix factorization modelmust be a global minimizer. Some scenarios under which the SNIG condition holds arepresented. Furthermore, we illustrate by an example when the SNIG condition may fail.