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Distributed subgradient method for multi‐agent optimization with quantized communication
Author(s) -
Li Jueyou,
Chen Guo,
Wu Zhiyou,
He Xing
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4044
Subject(s) - subgradient method , quantization (signal processing) , convex function , mathematical optimization , mathematics , convergence (economics) , convex optimization , constraint (computer aided design) , optimization problem , function (biology) , regular polygon , distributed algorithm , computer science , algorithm , distributed computing , geometry , evolutionary biology , economics , biology , economic growth
This paper focuses on a distributed optimization problem associated with a time‐varying multi‐agent network with quantized communication, where each agent has local access to its convex objective function, and cooperatively minimizes a sum of convex objective functions of the agents over the network. Based on subgradient methods, we propose a distributed algorithm to solve this problem under the additional constraint that agents can only communicate quantized information through the network. We consider two kinds of quantizers and analyze the quantization effects on the convergence of the algorithm. Furthermore, we provide explicit error bounds on the convergence rates that highlight the dependence on the quantization levels. Finally, some simulation results on a l 1 ‐regression problem are presented to demonstrate the performance of the algorithm. Copyright © 2016 John Wiley & Sons, Ltd.