Matrix-valued distributed stochastic optimization with constraints  

作　　者：Zicong XIA Yang LIU Wenlian LU Weihua GUI 

机构地区：[1]Key Laboratory of Intelligent Education Technology and Application of Zhejiang Province,Zhejiang Normal University,Jinhua 321004,China [2]School of Mathematical Sciences,Zhejiang Normal University,Jinhua 321004,China [3]School of Mathematical Sciences,Fudan University,Shanghai 200433,China [4]School of Automation,Central South University,Changsha 410083,China

出　　处：《Frontiers of Information Technology & Electronic Engineering》2023年第9期1239-1252,共14页信息与电子工程前沿（英文版）

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)。

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.

关 键 词：Distributed optimization Matrix-valued optimization Stochastic optimization Penalty method Gossip model 

分 类 号：O224[理学—运筹学与控制论]