带量化的分布式PUSH-SUM次梯度算法  

Distributed Push-Sum Subgradient Algorithm with Quantized Information

作　　者：黄继英 李觉友 HUANG Ji-ying;LI Jue-you(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China;Pengzhou No.1 Middle School,Pengzhou Sichuan 611930,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331 [2]彭州市第一中学,四川彭州611930

出　　处：《西南大学学报（自然科学版）》2020年第9期106-114,共9页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金青年项目(11971083);重庆市教委科学技术研究项目(KJQN201800520).

摘　　要：考虑了个体之间只能交换被量化过后的信息,并结合push-sum通讯机制和分布式次梯度算法,提出了带确定型量化的分布式push-sum次梯度算法,证明了当步长满足一定条件时,每个个体的状态收敛到网络最优解的邻域内.数值实验表明量化精度越高,越接近最优.In a time-varying directed graph,this paper studies the problem for minimizing the sum of several local convex objective functions,which are known to each agent accordingly.In the real communication network,due to the bandwidth limitation of communication,each agent can only exchangequantized information with its neighbors.Combining the push-sum communication mechanism and distributed subgradient algorithm,a distributed push-sum subgradient algorithm with deterministic quantization is proposedin this paper.It is proved that ifthe step size satisfies a certain condition,the state of each agent converges to the neighborhood of the optimal solution of the problem.A numerical experiment shows that the higher the quantization precision,the closer it isto the optima.

关 键 词：分布式优化 量化 push-sum算法 有向网络 

分 类 号：O224[理学—运筹学与控制论]