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.
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。
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The data that support the findings of this study are available from the corresponding author upon reasonable request.
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Zicong XIA, Yang LIU, and Wenlian LU designed the research. Zicong XIA processed the data. Zicong XIA and Yang LIU drafted the paper. Wenlian LU and Weihua GUI helped organize the paper. Yang LIU and Weihua GUI revised and finalized the paper.
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Yang LIU is a guest editor of this special feature, and he was not involved with the peer review process of this manuscript. Zicong XIA, Yang LIU, Wenlian LU, and Weihua GUI declare that they have no conflict of interest.
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Project supported by the National Natural Science Foundation of China (No. 62173308), the Natural Science Foundation of Zhejiang Province, China (Nos. LR20F030001 and LD19A010001), and the Jinhua Science and Technology Project, China (No. 2022-1-042)
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Xia, Z., Liu, Y., Lu, W. et al. Matrix-valued distributed stochastic optimization with constraints. Front Inform Technol Electron Eng 24, 1239–1252 (2023). https://doi.org/10.1631/FITEE.2200381
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DOI: https://doi.org/10.1631/FITEE.2200381