引用本文:邓文,李伟健,曾宪琳,洪奕光.矩阵方程的分布式求解算法研究概述[J].控制理论与应用,2021,38(11):1695~1706.[点击复制]
DENG Wen,LI Wei-jian,ZENG Xian-lin,HONG Yi-guang.A survey of distributed algorithms for solving matrix equations[J].Control Theory and Technology,2021,38(11):1695~1706.[点击复制]
矩阵方程的分布式求解算法研究概述
A survey of distributed algorithms for solving matrix equations
摘要点击 2887  全文点击 815  投稿时间：2021-07-26  修订日期：2021-11-19
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DOI编号  10.7641/CTA.2021.10671
  2021,38(11):1695-1706
中文关键词  分布式优化  矩阵方程  多智能体网络  分布式算法
英文关键词  distributed optimization  matrix equation  multi-agent network  distributed algorithm
基金项目  上海重大专项(2021SHZDZX0100), 国家自然科学基金项目(61733018, 62073035)资助.
作者单位E-mail
邓文 同济大学电子与信息工程学院控制科学与工程系, 上海自主智能无人系统科学中心 wdeng@tongji.edu.cn 
李伟健 中国科学技术大学自动化系  
曾宪琳* 北京理工大学自动化学院 xianlin.zeng@bit.edu.cn 
洪奕光 同济大学电子与信息工程学院控制科学与工程系, 上海自主智能无人系统科学中心  
中文摘要
      近年来, 随着大规模网络的兴起和分布式优化理论的广泛应用, 矩阵方程的分布式求解算法研究也受到了 越来越多的重视. 矩阵方程的计算求解在理论和工程领域都有着重要的意义. 在多智能体网络下的分布式计算问题 中, 矩阵方程中的数据信息按照各种方式进行划分, 单个智能体只能够获取其中的一份数据, 然后通过与其邻居智 能体进行信息交互, 最终合作求解出不同类型的符合方程要求的解. 本文集中讨论了近几年来针对线性代数方程、 几类不带约束和带约束线性矩阵方程、以及其他矩阵相关的分布式计算和求解问题, 介绍了投影一致方法、转化成 分布式优化问题再求解的方法、以及针对特殊矩阵如稀疏矩阵的信息传递方法等分布式算法设计方法. 最后, 简要 总结全文以及对分布式矩阵计算方向的研究进行了展望.
英文摘要
      In recent years, with the rise of large-scale networks and the widespread application of distributed optimization theory, distributed algorithms for solving matrix equations have received increasing research attention. The computation of matrix equations is of great importance in both theoretical and engineering fields. In the distributed computation over multi-agent networks, the data information of matrix equations is partitioned in various ways. Each agent is able to obtain only one partition of the data and communicate with its neighbors, but all the agents can cooperatively solve different types of solutions as required. In this survey, we focus on the distributed algorithms in recent matrix computation problems, such as linear algebraic equations, several types of unconstrained and constrained linear matrix equations, and other matrix-related problems. We introduce distributed algorithms such as projection with consensus, distributed optimization transformation, and special methods such as message passing methods for sparse ones. Finally, we give a brief summary and an outlook on the research area of distributed matrix computation.