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 $\epsilon$-exact penalty function to address the inequality constraints and derive an explicit lower bound on the penalty function weight to guarantee convergence to $\epsilon$-neighborhood of the global minimum value of the cost. A numerical example demonstrates our results.

翻译：我们建议对一组集束剂组成的网络,每个集束剂组成的一组子试剂构成一个限制的锥形优化问题采取分配式解决办法。集束剂的通信范围是,它们可以形成一个连接的无方向的图形表示学。优化问题的总成本是每个集束子剂的本地锥形成本之和。我们寻求在一系列同系物的平等制约下最大限度地降低这一成本,以及一套对等不平等的限制,规定在存在这种界限时决定变量的界限。我们设计了一个基于集束的框架,以大幅降低通信和计算成本。我们提议的分布式计算法是一种新的连续时间算法,它与增强的拉格朗加法相联系。当本地成本功能是同系时,当它们具有强烈的同系物,并且具有利普施氏梯度时,它就会变得同步。此外,我们用一个美元=epslon-exact处罚功能来解决不平等制约,并获得明确的较低刑罚重量约束,以保障我们最低值的美元/epsilon-Igrental exal-gillon exal-grual-gleglegal-galgal-gal-galgal-gal-gal-galgalgalgal-galgalgalgalgalgal-galgalgalgalgalgalgalgalgalgal) 。