In this paper, we consider a general challenging distributed optimization setup arising in several important network control applications. Agents of a network want to minimize the sum of local cost functions, each one depending on a local variable, subject to local and coupling constraints, with the latter involving all the decision variables. We propose a novel fully distributed algorithm based on a relaxation of the primal problem and an elegant exploration of duality theory. Despite its complex derivation, based on several duality steps, the distributed algorithm has a very simple and intuitive structure. That is, each node finds a primal-dual optimal solution pair of a local relaxed version of the original problem and then updates suitable auxiliary local variables. We prove that agents asymptotically compute their portion of an optimal (feasible) solution of the original problem. This primal recovery property is obtained without any averaging mechanism typically used in dual decomposition methods. To corroborate the theoretical results, we show how the methodology applies to an instance of a distributed model-predictive control scheme in a microgrid control scenario.

中文翻译：

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约束耦合的分布式优化：一种松弛和对偶方法

在本文中，我们考虑了在几个重要的网络控制应用程序中出现的具有挑战性的通用分布式优化设置。网络的代理希望将局部成本函数的总和最小化，每个局部函数取决于局部变量，并受局部和耦合约束，后者涉及所有决策变量。我们提出了一种新颖的完全分布式算法，该算法基于原始问题的松弛和对偶理论的精妙探索。尽管基于多个对偶步骤进行了复杂的推导，但分布式算法仍具有非常简单直观的结构。即，每个节点找到原始问题的局部松弛版本的本对偶最优解对，然后更新合适的辅助局部变量。我们证明了代理渐近地计算了原始问题的最优（可行）解的部分。在没有双重分解方法中通常使用的任何平均机制的情况下获得此原始恢复特性。为了证实理论结果，我们展示了该方法如何应用于微电网控制场景中的分布式模型预测控制方案的实例。