非平衡有向网络的完全分布式凸优化

A fully distributed convex optimization algorithm over the unbalanced directed network

分布式凸优化问题的目的是如何以分布式方法最小化局部智能体成本函数和,而现有分布式算法的控制步长选取依赖于系统智能体个数、伴随矩阵等全局性信息,有悖于分布式算法的初衷.针对此问题,提出一种基于非平衡有向网络的完全分布式凸优化算法(FDCOA).基于多智能体一致性理论和梯度跟踪技术,设计了一种非负余量迭代策略,使得FDCOA的控制步长收敛范围仅与智能体局部信息相关,进而实现控制步长的分布式设置.进一步分析了FDCOA在固定强连通和时变强连通网络情形下的收敛性.仿真结果表明本文构建的分布式控制步长选取方法对FDCOA在有向非平衡下的分布式凸优化问题是有效的.

The aim of the distributed convex optimization problem is how to minimize the sum of all local agent cost functions,and however,the control step-size of the existing distributed algorithms is related to the global information,such as agent numbers of system,adjacency matrix,which is contracted to the distributed algorithm.For solving this problem,a fully distributed convex optimization algorithm(FDCOA)is proposed over the unbalanced directed network.Based on the multi-agent consensus theory and gradient tracking technology,a non-negative surplus iteration scheme is designed to make the convergence range of the control step-size only related to the local information of each agent,and then to realize the uncoordinated and distributed setting of the control step-size.Further,the convergence analysis of the FDCOA is given for both fixed and time-varying strongly connected digraphs.The experimental results show that the designed distributed selection method of the control step-size is effective for the application of FDCOA to the distributed convex optimization problems under an unbalanced directed network.