基于非光滑分析的凸优化问题分布式量化算法  

Distributed Quantization Algorithm for Convex Optimization Problems Based on Non-smooth Analysis

作　　者：袁君萍 李德权 

机构地区：[1]安徽理工大学数学与大数据学院,安徽淮南232001

出　　处：《佳木斯大学学报（自然科学版）》2018年第1期153-157,共5页Journal of Jiamusi University：Natural Science Edition

基　　金：高校学科(专业)拔尖人才学术资助重点项目(gxbj ZD2016049)

摘　　要：研究了量化信息通信情况下的多个体网络分布式凸优化算法。个体之间通过固定拓扑无向图交流信息,利用边laplacian矩阵,将个体的状态信息转化为个体间的边状态信息;进而对边的状态信息进行量化,而信息量化导致原成本函数产生了非光滑问题,通过构造合适的Lyapunov函数并引入了非光滑分析求其梯度,证明了在所提优化算法作用下整个网络系统的状态最终一致有界。The distributed optimization problem of a sum of convex cost functions with quantized interactions among agents is studied. The network of the agents interacting over an undirected graph, the state information of the agents is transformed into the edge state information between the agents by using the edge laplacian matrix, then the state information of the edges are quantized, and the original cost functions is generated to produce non - smooth problems, then we select the proper Lyapunov function and introduce the non - smooth analysis to find the gradient. Finally, the algorithm is proved to be uniformly bounded.

关 键 词：量化 边laplacian 非光滑分析 一致有界 

分 类 号：O224[理学—运筹学与控制论]