使用网络节点信息传递策略的分布式优化新算法  

New distributed optimization algorithm using network node information transfer strategy

作　　者：马文龙 付敏跃[2] 张焕水[1] MA Wen-long;FU Min-yue;ZHANG Huan-shui(School of Control Science and Engineering,Shandong University,Jinan Shandong 250100,China;School of Electrical Engineering and Computing,University of Newcastle,NSW 2308,Australia)

机构地区：[1]山东大学控制科学与工程学院,山东济南250100 [2]纽卡斯尔大学电子工程与计算学院,澳大利亚新南威尔士州2308

出　　处：《控制理论与应用》2021年第12期2001-2009,共9页Control Theory & Applications

基　　金：国家自然科学基金项目(61633014,61573221,U1701264)资助。

摘　　要：本文基于统计学习中众所周知的信度传播理论来研究非线性凸优化问题的分布式算法.通过对优化问题中的网络图中节点上和节点之间的计算以及信息传递过程的深入研究,结合信度传播理论得出适合分布式优化算法的信息传递策略.在集中式经典牛顿法和原始对偶方法框架下,所提分布式算法通过网络中的信息传递策略来完成设计.所提的分布式牛顿-拉夫森算法在无圈连通图情形下是集中式牛顿法的分布式实现.所提分布式原始对偶算法在无圈图情形下有集中式原始对偶算法的收敛效果,且对于有圈连通图也有较好的适应性和鲁棒性.仿真实验说明了我们所提信息传递策略和算法的收敛效果和适合的应用场景.This paper is based on the well-known belief propagation theory in statistical learning to study distributed algorithms for nonlinear convex optimization problems.Through in-depth research on the calculation and information transfer process on and between nodes in the network graph of the optimization problem,combined with the belief propagation theory,an information transfer strategy suitable for distributed optimization algorithms is obtained.Under the framework of the centralized classic Newton method and the primal-dual method,the proposed distributed algorithm completes the design using the information transmission in the network.The proposed distributed Newton-Raphson algorithm is a distributed implementation of the centralized Newton method in the case of acyclic connected graphs.The proposed distributed primitive dual algorithm has a similar convergence property of the centralized primal-dual algorithm in the case of acyclic graphs,and it also has better adaptability and robustness for cyclic connected graphs.The simulation experiment illustrates the convergence property and suitable application scenarios of our proposed information transmission strategy and algorithms.

关 键 词：多自主体系统 凸优化 牛顿-拉夫森方法 原始对偶方法 信度传播 

分 类 号：O224[理学—运筹学与控制论]