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Frontiers of Information Technology & Electronic Engineering 

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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 , 1998, -1(5): .

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author="Zicong XIA, Yang LIU, Wenlian LU, Weihua GUI",
journal="Frontiers of Information Technology & Electronic Engineering",
volume="-1",
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pages="",
year="1998",
publisher="Zhejiang University Press & Springer",
doi="10.1631/FITEE.2200381"
}

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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 delineated to demonstrate the viability of the main results.

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