引用本文:马文龙,付敏跃,张焕水.使用网络节点信息传递策略的分布式优化新算法[J].控制理论与应用,2021,38(12):2001~2009.[点击复制]
MA Wen-long,FU Min-yue,ZHANG Huan-shui.New distributed optimization algorithm using network node information transfer strategy[J].Control Theory and Technology,2021,38(12):2001~2009.[点击复制]
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
摘要点击 1716  全文点击 415  投稿时间：2020-09-06  修订日期：2021-04-08
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DOI编号  10.7641/CTA.2021.00596
  2021,38(12):2001-2009
中文关键词  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
英文关键词  multi-agent systems  convex optimization  Newton–Raphson method  primal-dual method  belief propagation
基金项目  国家自然科学基金项目(61633014, 61573221, U1701264)资助.
作者单位E-mail
马文龙 山东大学 sqsyxiaoma@163.com 
付敏跃* 纽卡斯尔大学  
张焕水 山东大学 hszhang@sdu.edu.cn 
中文摘要
      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.
英文摘要
      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.