A proximal point algorithm revisit on the alternating direction method of multipliers
A proximal point algorithm revisit on the alternating direction method of multipliers
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DOI：
10.1007/s11425-013-4683-0
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发表时间：
2013-08
期刊：
影响因子：
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通讯作者：
Xingju Cai;G. Gu;B. He;Xiaoming Yuan
中科院分区：
文献类型：
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作者：
Xingju Cai;G. Gu;B. He;Xiaoming Yuan
交替方向乘子法（ADMM）是求解具有可分目标函数和线性约束的凸规划问题的一个基准算法。在文献中，它已被说明为应用程序的近点算法（PPA）的对偶问题的模型正在考虑中。本文表明，ADMM也可以被视为PPA的原始模型的一个应用程序与定制的选择的最接近的参数。因此，ADMM的这种原始说明是对文献中其双重说明的补充。这种PPA重访ADMM从原始的角度也使我们能够恢复广义ADMM提出的Eckstein和Bertsekas容易。本文对Eckstein和Bertsekas的广义ADMM作了一点推广，得到了遍历意义下的最坏情况O（1/t）收敛速度.
The alternating direction method of multipliers (ADMM) is a benchmark for solving convex programming problems with separable objective functions and linear constraints. In the literature it has been illustrated as an application of the proximal point algorithm (PPA) to the dual problem of the model under consideration. This paper shows that ADMM can also be regarded as an application of PPA to the primal model with a customized choice of the proximal parameter. This primal illustration of ADMM is thus complemental to its dual illustration in the literature. This PPA revisit on ADMM from the primal perspective also enables us to recover the generalized ADMM proposed by Eckstein and Bertsekas easily. A worst-caseO(1/t) convergence rate in ergodic sense is established for a slight extension of Eckstein and Bertsekas’s generalized ADMM.