论文标题
分布式优化基于双近端梯度方法的多群集网络中的耦合约束
Distributed Optimization with Coupling Constraints in Multi-Cluster Networks Based on Dual Proximal Gradient Method
论文作者
论文摘要
在这项工作中，我们考虑在具有多个集群的多代理网络中解决分布式优化问题。在每个群集中，相关代理可以通过共同的决策变量合作优化可分离的复合函数。同时，整个网络的全球成本函数被认为与群集中的仿射耦合约束相关。为了解决这个问题，我们通过诉诸双重问题提出了一个基于群集的双重近端梯度算法，当每个集群中的代理达成最佳策略和全局耦合约束时，都可以优化全局成本函数。此外，拟议的算法允许代理只与直接邻居进行交流。讨论了所提出的算法具有简单结构成本函数的计算复杂性，并保证具有速率O（1/t）的千古收敛（t是迭代的索引）。
In this work, we consider solving a distributed optimization problem in a multi-agent network with multiple clusters. In each cluster, the involved agents cooperatively optimize a separable composite function with a common decision variable. Meanwhile, a global cost function of the whole network is considered associated with an affine coupling constraint across the clusters. To solve this problem, we propose a cluster-based dual proximal gradient algorithm by resorting to the dual problem, where the global cost function is optimized when the agents in each cluster achieve an agreement on the optimal strategy and the global coupling constraint is satisfied. In addition, the proposed algorithm allows the agents to only communicate with their immediate neighbors. The computational complexity of the proposed algorithm with simple-structured cost functions is discussed and an ergodic convergence with rate O(1/T) is guaranteed (T is the index of iterations).
