Iteratively Linearized Reweighted Alternating Direction Method of Multipliers for a Class of Nonconvex Problems

作者：Sun, Tao^*; Jiang, Hao; Cheng, Lizhi; Zhu, Wei

来源：IEEE Transactions on Signal Processing, 2018, 66(20): 5380-5391.

DOI：10.1109/TSP.2018.2868269

• Alternating direction method of multipliers
• Iteratively reweighted algorithm
• Nonconvex and nonsmooth minimization
• Kurdyka-Lojasiewicz property
• Semi-algebraic functions

In this paper, we consider solving a class of nonconvex and nonsmooth problems frequently appearing in signal processing andmachine learning research. The traditional alternating directionmethod of multipliers encounters troubles in both mathematics and computations in solving the nonconvex and nonsmooth subproblem. In view of this, we propose a reweighted alternating direction method of multipliers. In this algorithm, all subproblems are convex and easy to solve. We also provide several guarantees for the convergence and prove that the algorithm globally converges to a critical point of an auxiliary function with the help of the Kurdyka-Lojasiewicz property. Several numerical results are presented to demonstrate the efficiency of the proposed algorithm.

• 出版日期2018-10-15
• 单位中国人民解放军国防科学技术大学; 湘潭大学