We propose a distributed solution for a constrained convex optimization problem over a network of clustered agents each consisted of a set of subagents. The communication range of the clustered agents is such that they can form a connected undirected graph topology. The total cost in this optimization problem is the sum of the local convex costs of the subagents of each cluster. We seek a minimizer of this cost subject to a set of affine equality constraints, and a set of affine inequality constraints specifying the bounds on the decision variables if such bounds exist. We design our distributed algorithm in a cluster-based framework which results in a significant reduction in communication and computation costs. Our proposed distributed solution is a novel continuous-time algorithm that is linked to the augmented Lagrangian approach. It converges asymptotically when the local cost functions are convex and exponentially when they are strongly convex and have Lipschitz gradients. Moreover, we use an $ϵ$-exact penalty function to address the inequality constraints and derive an explicit lower bound on the penalty function weight to guarantee convergence to $ϵ$-neighborhood of the global minimum value of the cost. A numerical example demonstrates our results.

我们提出了一个针对集群式智能体网络上约束凸优化问题的分布式解决方案，每个集群式智能体都由一组子智能体组成。集群代理的通信范围使得它们可以形成连接的无向图拓扑。此优化问题中的总成本是每个群集的子代理的局部凸成本的总和。我们寻求此成本的最小化器，它受一组仿射等式约束和一组仿射不等式约束的约束，这些约束指定了决策变量的边界（如果存在）。我们在基于集群的框架中设计分布式算法，从而大大降低了通信和计算成本。我们提出的分布式解决方案是一种新颖的连续时间算法，该算法链接到增强型拉格朗日方法。当局部成本函数为凸时，它渐近收敛；当它们为强凸且具有Lipschitz梯度时，它呈指数收敛。此外，我们使用$ϵ$-精确罚函数以解决不等式约束，并得出罚函数权重的显式下界，以确保收敛到 $ϵ$-成本的全球最小值附近。数值例子说明了我们的结果。