Abstract

We study finite-time performance of a recently proposed distributed dual subgradient (DDSG) method for convex-constrained multi-agent optimization problems. The algorithm enjoys performance guarantees on the last primal iterate, as opposed to those derived for ergodic means for standard DDSG algorithms. Our work improves the recently published convergence rate of \({{\mathcal {O}}}(\log T/\sqrt{T})\) with decaying step-sizes to \({{\mathcal {O}}}(1/\sqrt{T})\) with constant step-size on a metric that combines sub-optimality and constraint violation. We then numerically evaluate the algorithm on three grid optimization problems. Namely, these are tie-line scheduling in multi-area power systems, coordination of distributed energy resources in radial distribution networks, and joint dispatch of transmission and distribution assets. The DDSG algorithm applies to each problem with various relaxations and linearizations of the power flow equations. The numerical experiments illustrate various properties of the DDSG algorithm–comparison with standard DDSG, impact of the number of agents, and why Nesterov-style acceleration can fail in DDSG settings.

中文翻译：

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具有平均的分布式双次梯度方法及其在网格优化中的应用

摘要

我们研究了最近提出的分布式双次梯度（DDSG）方法的有限时间性能，用于解决凸约束多智能体优化问题。该算法在最后一次原始迭代上享有性能保证，这与标准 DDSG 算法的遍历均值派生的性能保证不同。我们的工作将最近发布的\({{\mathcal {O}}}(\log T/\sqrt{T})\)的收敛速度提高到\({{\mathcal {O}}} (1/\sqrt{T})\)在结合了次优性和约束违规的度量上具有恒定的步长。然后，我们对三个网格优化问题的算法进行数值评估。即多区域电力系统联络线调度、放射状配电网分布式能源协调、输配电资产联合调度等。DDSG 算法适用于功率流方程的各种松弛和线性化的每个问题。数值实验说明了 DDSG 算法的各种属性 - 与标准 DDSG 的比较、代理数量的影响以及为什么 Nesterov 式加速在 DDSG 设置中会失败。