Distributed Primal-Dual Method for Convex Optimization With Coupled Constraints
Distributed Primal-Dual Method for Convex Optimization With Coupled Constraints
复制标题
耦合约束凸优化的分布式原对偶方法
DOI：
10.1109/tsp.2021.3123888
复制
发表时间：
2022
影响因子：
5.4
通讯作者：
Changyin Sun
中科院分区：
文献类型：
--
作者：
Yanxu Su;Qingling Wang;Changyin Sun
分布式原-对偶方法已广泛应用于求解大规模约束优化问题。现有的大多数结果集中在解耦约束问题。最近的一些工作研究了可分离全局耦合约束问题。本文考虑了网络上具有全局耦合约束的分布式优化问题，而不要求全局耦合约束的可分性。这是可能的约束违反的本地估计。为了解决这样的问题，我们提出了一个原始-对偶算法在增广拉格朗日框架，结合平均共识技术。我们首先建立了一个非遍历收敛速度<inline-formula><tex-math notation="LaTeX">$\mathcal {O}（1/k）$</tex-math></inline-formula>的目标残差求解分布式约束凸优化问题，其中<inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>是迭代计数器。具体来说，全局目标函数是局部凸成本和可能非光滑成本的总和，耦合约束是局部线性等式约束的总和。数值结果说明了所提出的方法的性能。
Distributed primal-dual methods have been widely used for solving large-scale constrained optimization problems. The majority of existing results focus on the problems with decoupled constraints. Some recent works have studied the problems subject to separable globally coupled constraints. This paper considers the distributed optimization problems with globally coupled constraints over networks without requiring the separability of the globally coupled constraints. This is made possible by the local estimates of the constraint violations. For solving such a problem, we propose a primal-dual algorithm in the augmented Lagrangian framework, combining the average consensus technique. We first establish a non-ergodic convergence rate of <inline-formula><tex-math notation="LaTeX">$\mathcal {O}(1/k)$</tex-math></inline-formula> in terms of the objective residual for solving a distributed constrained convex optimization problem, where <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> is the iteration counter. Specifically, the global objective function is the aggregate of the local convex and possibly non-smooth costs, and the coupled constraint is the sum of the local linear equality constraints. The numerical results illustrate the performance of the proposed method.