论文标题
用于求解可分离凸优化的对称近端ADMM的不精确版本
An inexact version of the symmetric proximal ADMM for solving separable convex optimization
论文作者
论文摘要
在本文中，我们提出和分析了对称近端交流方向方法（ADMM）的不精确版本，以解决线性约束优化问题。基本上，该方法允许其第一个子问题不截然不1，以便满足相对近似标准。就迭代编号$ k $而言，我们建立了全局$ \ MATHCAL {O}（1/ \ sqrt {k}）$ coptwise和$ \ Mathcal {o}（1/ {k}）$ ergodic收敛速率，用于加入参数的域名域，这是一致的，该域是一致的。由于对称近端ADMM可以看作是一类ADMM变体，因此新算法以及其收敛速率推广，尤其是文献中的许多其他算法。报道了该方法的实际优势的数值实验。据我们所知，这项工作是第一个研究对称近端ADMM的不精确版本的作品。
In this paper, we propose and analyze an inexact version of the symmetric proximal alternating direction method of multipliers (ADMM) for solving linearly constrained optimization problems. Basically, the method allows its first subproblem to be solved inexactly in such way that a relative approximate criterion is satisfied. In terms of the iteration number $k$, we establish global $\mathcal{O} (1/ \sqrt{k})$ pointwise and $\mathcal{O} (1/ {k})$ ergodic convergence rates of the method for a domain of the acceleration parameters, which is consistent with the largest known one in the exact case. Since the symmetric proximal ADMM can be seen as a class of ADMM variants, the new algorithm as well as its convergence rates generalize, in particular, many others in the literature. Numerical experiments illustrating the practical advantages of the method are reported. To the best of our knowledge, this work is the first one to study an inexact version of the symmetric proximal ADMM.
