Matrix-valued distributed stochastic optimization with constraints

Zicong XIA; Yang LIU; Wenlian LU; Weihua GUI

doi:10.1631/FITEE.2200381

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Matrix-valued distributed stochastic optimization with constraints

Special Feature on Intelligent Dynamics Optimization Methods and Their Applications | Updated：2023-09-21

- Matrix-valued distributed stochastic optimization with constraints
  Cover Article
- 带约束的矩阵值分布式随机优化
- Frontiers of Information Technology & Electronic Engineering Vol. 24, Issue 9, Pages: 1239-1252(2023)
- 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：
- DOI：10.1631/FITEE.2200381
  CLC： O224
- Received：07 September 2022，
  
  Accepted：28 October 2022，
  
  Published Online：12 August 2023，
  
  Published：0 September 2023
- Accepted：
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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：

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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Keywords

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