Liu Jing, Duan Yongrui, Sun Min
School of Economics and Management, Tongji University, Shanghai, 200092 P.R. China.
School of Data Sciences, Zhejiang University of Finance and Economics, Zhejiang, 310018 P.R. China.
J Inequal Appl. 2017;2017(1):129. doi: 10.1186/s13660-017-1405-0. Epub 2017 Jun 5.
This paper introduces a symmetric version of the generalized alternating direction method of multipliers for two-block separable convex programming with linear equality constraints, which inherits the superiorities of the classical alternating direction method of multipliers (ADMM), and which extends the feasible set of the relaxation factor of the generalized ADMM to the infinite interval [Formula: see text]. Under the conditions that the objective function is convex and the solution set is nonempty, we establish the convergence results of the proposed method, including the global convergence, the worst-case [Formula: see text] convergence rate in both the ergodic and the non-ergodic senses, where denotes the iteration counter. Numerical experiments to decode a sparse signal arising in compressed sensing are included to illustrate the efficiency of the new method.
本文介绍了一种用于具有线性等式约束的两模块可分凸规划的广义乘子交替方向法的对称版本，它继承了经典乘子交替方向法（ADMM）的优势，并将广义ADMM的松弛因子可行集扩展到无限区间[公式：见原文]。在目标函数为凸函数且解集非空的条件下，我们建立了所提方法的收敛结果，包括全局收敛性、遍历和非遍历意义下的最坏情况[公式：见原文]收敛速率，其中[公式：见原文]表示迭代计数器。还包括用于解码压缩感知中出现的稀疏信号的数值实验，以说明新方法的有效性。
