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论文类型：期刊论文

发表时间：2015-07-04

发表刊物：OPTIMIZATION METHODS & SOFTWARE

收录刊物：SCIE、EI

卷号：30

期号：4

页面范围：682-705

ISSN号：1055-6788

关键字：low-rank problem; l(2)(2)-l(p)(p) minimization; majorization method; lower bound analysis; smoothing method

摘要：In this paper, we consider the l(2)(2)-l(p)(p) (with p is an element of(0, 1)) matrix minimization for recovering the low-rank matrices. A smoothing approach for solving this non-smooth, non-Lipschitz and non-convex l(2)(2)-l(p)(p) optimization problem is developed, in which the smoothing parameter is treated as a decision variable and a majorization method is adopted to solve the smoothing problem. The convergence theorem shows that any accumulation point of the sequence generated by the proposed approach satisfies the first-order necessary optimality condition of the l(2)(2)-l(p)(p) problem. As an application, we use the proposed smoothing majorization method to solve the famous matrix completion problems. Numerical results indicate that our algorithm can solve the test problems efficiently.