带约束的矩阵值分布式随机优化

夏子聪; 刘洋; 卢文联; 桂卫华

doi:10.1631/FITEE.2200381

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带约束的矩阵值分布式随机优化

专题 | Updated：2023-09-21

- 带约束的矩阵值分布式随机优化
  Cover Article
- Matrix-valued distributed stochastic optimization with constraints
- 信息与电子工程前沿（英文） 2023年24卷第9期页码：1239-1252
- Affiliations：
  
  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
- Author bio：
  
  E-mail: 201531700128@zjnu.edu.cn
  ‡Corresponding author
  wenlian@fudan.edu.cn
  gwh@csu.edu.cn
- Funds：
  
  National Natural Science Foundation of China(62173308);Natural Science Foundation of Zhejiang Province, China(LR20F030001;LD19A010001);Jinhua Science and Technology Project, China(2022-1-042)
- DOI：10.1631/FITEE.2200381
  中图分类号： O224
- 收稿：2022-09-07，
  
  录用：2022-10-28，
  
  网络出版：2023-08-12，
  
  纸质出版：2023-09-0
- Accepted：
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夏子聪, 刘洋, 卢文联, 等. 带约束的矩阵值分布式随机优化[J]. 信息与电子工程前沿（英文）, 2023,24(9):1239-1252.

Zicong XIA, Yang LIU, Wenlian LU, et al. Matrix-valued distributed stochastic optimization with constraints[J]. Frontiers of Information Technology & Electronic Engineering, 2023, 24(9): 1239-1252.
夏子聪, 刘洋, 卢文联, 等. 带约束的矩阵值分布式随机优化[J]. 信息与电子工程前沿（英文）, 2023,24(9):1239-1252. DOI： 10.1631/FITEE.2200381.

Zicong XIA, Yang LIU, Wenlian LU, et al. Matrix-valued distributed stochastic optimization with constraints[J]. Frontiers of Information Technology & Electronic Engineering, 2023, 24(9): 1239-1252. DOI： 10.1631/FITEE.2200381.

摘要

本文研究带有不等式约束和等式约束的矩阵值分布随机优化问题。其中，问题的目标函数是具有随机变量的多个矩阵值函数的和，并以分布式方式解决了该问题。本文推导了处理约束的惩罚方法，并提出选择可行惩罚函数和惩罚增益的原则。针对随机优化问题，提出一种基于gossip模型的分布式优化算法，并对其收敛性进行证明和分析。最后，为验证所提算法的可行性，本文提供了两个数值示例。

Abstract

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.

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