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Date:2019-03-09

Indexed by:Journal Article

Date of Publication:2015-07-04

Journal:OPTIMIZATION METHODS & SOFTWARE

Included Journals:EI、SCIE

Volume:30

Issue:4

Page Number:682-705

ISSN:1055-6788

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

Abstract: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.