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CLC number: O224

On-line Access: 2023-06-21

Received: 2022-09-07

Revision Accepted: 2023-09-21

Crosschecked: 2022-10-28

Cited: 0

Clicked: 819

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Zicong XIA

https://orcid.org/0000-0001-9943-5087

Yang LIU

https://orcid.org/0000-0003-3761-0104

Wenlian LU

https://orcid.org/0000-0003-1880-6240

Weihua GUI

https://orcid.org/0000-0002-5337-6445

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Frontiers of Information Technology & Electronic Engineering  2023 Vol.24 No.9 P.1239-1252

http://doi.org/10.1631/FITEE.2200381


Matrix-valued distributed stochastic optimization with constraints


Author(s):  Zicong XIA, Yang LIU, Wenlian LU, Weihua GUI

Affiliation(s):  Key Laboratory of Intelligent Education Technology and Application of Zhejiang Province, Zhejiang Normal University, Jinhua 321004, China; more

Corresponding email(s):   201531700128@zjnu.edu.cn, liuyang@zjnu.edu.cn, wenlian@fudan.edu.cn, gwh@csu.edu.cn

Key Words:  Distributed optimization, Matrix-valued optimization, Stochastic optimization, Penalty method, Gossip model


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Zicong XIA, Yang LIU, Wenlian LU, Weihua GUI. Matrix-valued distributed stochastic optimization with constraints[J]. Frontiers of Information Technology & Electronic Engineering, 2023, 24(9): 1239-1252.

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publisher="Zhejiang University Press & Springer",
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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.

带约束的矩阵值分布式随机优化

夏子聪1,2,刘洋1,2,卢文联3,桂卫华4
1浙江师范大学浙江省智能教育技术与应用重点实验室,中国金华市,321004
2浙江师范大学数学科学学院,中国金华市,321004
3复旦大学数学科学学院,中国上海市,200433
4中南大学自动化学院,中国长沙市,410083
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。

关键词:分布式优化;矩阵值优化;随机优化;罚函数法;Gossip模型

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

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