Iteratively Linearized Reweighted Alternating Direction Method of Multipliers for a Class of Nonconvex Problems
Iteratively Linearized Reweighted Alternating Direction Method of Multipliers for a Class of Nonconvex Problems
复制标题
一类非凸问题的迭代线性重加权交替方向乘子法
DOI：
10.1109/tsp.2018.2868269
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发表时间：
2018
影响因子：
5.4
通讯作者：
Wei Zhu
中科院分区：
文献类型：
--
作者：
Tao Sun;Hao Jiang;Lizhi Cheng;Wei Zhu
本文考虑解决信号处理和机器学习研究中经常出现的一类非凸非光滑问题。传统的乘法器交替方向法在求解非凸非光滑子问题时遇到了数学和计算上的困难。鉴于此，我们提出了一种重加权的乘法器交替方向法。在该算法中，所有子问题都是凸的，易于求解。给出了收敛性的若干保证，并利用Kurdyka -Łojasiewicz性质证明了算法全局收敛于辅助函数的一个临界点。数值结果验证了该算法的有效性。
In this paper, we consider solving a class of nonconvex and nonsmooth problems frequently appearing in signal processing and machine learning research. The traditional alternating direction method 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–Łojasiewicz property. Several numerical results are presented to demonstrate the efficiency of the proposed algorithm.