A smoothing majorization method for l(2)(2)-l(p)(p) matrix minimization

作者：Lu, Yue^*; Zhang, Liwei; Wu, Jia

来源：Optimization Methods and Software, 2015, 30(4): 682-705.

DOI：10.1080/10556788.2014.967235

• low-rank problem
• l(2)(2)-l(p)(p) minimization
• majorization method
• lower bound analysis
• smoothing method

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.

• 出版日期2015
• 单位大连理工大学