Matrix-valued distributed stochastic optimization with constraints

作     者：Zicong XIA Yang LIU Wenlian LU Weihua GUI Zicong XIA;Yang LIU;Wenlian LU;Weihua GUI

作者机构：Key Laboratory of Intelligent Education Technology and Application of Zhejiang ProvinceZhejiang Normal UniversityJinhua 321004China School of Mathematical SciencesZhejiang Normal UniversityJinhua 321004China School of Mathematical SciencesFudan UniversityShanghai 200433China School of AutomationCentral South UniversityChangsha 410083China 

出 版 物：《信息与电子工程前沿:英文版》 (Frontiers of Information Technology & Electronic Engineering)

年 卷 期：2023年第24卷第9期

页      面：1239-1252页

核心收录：

学科分类：0711[理学-系统科学] 07[理学] 070105[理学-运筹学与控制论] 0701[理学-数学] 0811[工学-控制科学与工程] 

基　　金：Project supported by the National Natural Science Foundation of China(No.62173308) the Natural Science Foundation of Zhejiang Province,China(Nos.LR20F030001 and LD19A010001) the Jinhua Science and Technology Project,China(No.2022-1-042)。 

主　　题：Distributed optimization Matrix-valued optimization Stochastic optimization Penalty method Gossip model 

摘      要：In this paper,we address matrix-valued distributed stochastic optimization with inequality and equality constraints,where the objective function is a sum of multiple matrix-valued functions with stochastic variables and the considered problems are solved in a distributed manner.A penalty method is derived to deal with the constraints,and a selection principle is proposed for choosing feasible penalty functions and penalty gains.A distributed optimization algorithm based on the gossip model is developed for solving the stochastic optimization problem,and its convergence to the optimal solution is analyzed rigorously.Two numerical examples are given to demonstrate the viability of the main results.