SNIG PROPERTY OF MATRIX LOW-RANK FACTORIZATION MODEL

• 来源期刊: 计算数学（英文版）
• 关键词: Low rank factorization Nonconvex optimization Second-order optimality condition Global minimizer
• 年，卷（期）: 2018,（3）
• 页码范围: 374-390
• 页数: 17页
• 语种: 英文
• DOI: 10.4208/jcm.1707-m2016-0796

摘要

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.