Geodesic
A stochastic mirror-descent algorithm for solving $AXB=C$ over an multi-agent system
Kybernetika, Tome 57 (2021) no. 2, pp. 256-271.

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In this paper, we consider a distributed stochastic computation of $AXB=C$ with local set constraints over an multi-agent system, where each agent over the network only knows a few rows or columns of matrixes. Through formulating an equivalent distributed optimization problem for seeking least-squares solutions of $AXB=C$, we propose a distributed stochastic mirror-descent algorithm for solving the equivalent distributed problem. Then, we provide the sublinear convergence of the proposed algorithm. Moreover, a numerical example is also given to illustrate the effectiveness of the proposed algorithm.
DOI : 10.14736/kyb-2021-2-0256
Classification : 68M15, 93A14
Keywords: distributed computation of matrix equation; multi-agent system; sublinear convergence; stochastic mirror descent algorithm 
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     title = {A stochastic mirror-descent algorithm for solving $AXB=C$ over an multi-agent system},
     journal = {Kybernetika},
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Wang, Yinghui; Cheng, Songsong. A stochastic mirror-descent algorithm for solving $AXB=C$ over an multi-agent system. Kybernetika, Tome 57 (2021) no. 2, pp. 256-271. doi : 10.14736/kyb-2021-2-0256. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2021-2-0256/

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