标题： 随机ADMM用于非光滑优化 显示英文标题

标题： Stochastic ADMM for Nonsmooth Optimization

摘要： 我们为在线性等式约束下具有非光滑凸可分离目标函数的优化问题提供了一个随机设置。 为了解决这些问题，我们提出了一种随机交替方向乘子法（ADMM）算法。 我们的算法适用于更广泛的非光滑凸函数，这些函数不一定通过直接最小化增广函数有闭式解。 我们还展示了在随机函数的各种结构假设下，我们的算法的收敛速率：$O(1/\sqrt{t})$对于凸函数，$O(\log t/t)$对于强凸函数。 与之前的研究相比，我们首次从目标值和可行性违反两个方面建立了ADMM算法的收敛速率。 显示英文摘要

摘要： We present a stochastic setting for optimization problems with nonsmooth convex separable objective functions over linear equality constraints. To solve such problems, we propose a stochastic Alternating Direction Method of Multipliers (ADMM) algorithm. Our algorithm applies to a more general class of nonsmooth convex functions that does not necessarily have a closed-form solution by minimizing the augmented function directly. We also demonstrate the rates of convergence for our algorithm under various structural assumptions of the stochastic functions: $O(1/\sqrt{t})$ for convex functions and $O(\log t/t)$ for strongly convex functions. Compared to previous literature, we establish the convergence rate of ADMM algorithm, for the first time, in terms of both the objective value and the feasibility violation.