This paper focuses on distributed consensus optimization problems with coupled constraints over time-varying multi-agent networks, where the global objective is the finite sum of all agents’ private local objective functions, and decision variables of agents are subject to coupled equality and inequality constraints and a compact convex subset. Each agent exchanges information with its neighbors and processes local data. They cooperate to agree on a consensual decision vector that is an optimal solution to the considered optimization problems. We integrate ideas behind dynamic average consensus and primal-dual methods to develop a distributed algorithm and establish its sublinear convergence rate. In numerical simulations, to illustrate the effectiveness of the proposed algorithm, we compare it with some related methods by the Neyman–Pearson classification problem.

本文重点研究时变多智能体网络上具有耦合约束的分布式共识优化问题，其中全局目标是所有智能体私有局部目标函数的有限和，智能体的决策变量受到耦合等式和不等式约束和一个紧凸子集。每个代理与其邻居交换信息并处理本地数据。他们合作达成一致的决策向量，该向量是所考虑的优化问题的最佳解决方案。我们整合动态平均共识和原对偶方法背后的思想来开发分布式算法并建立其次线性收敛率。在数值模拟中，为了说明所提出算法的有效性，我们通过 Neyman-Pearson 分类问题将其与一些相关方法进行比较。