Geodesic
A penalty ADMM with quantized communication for distributed optimization over multi-agent systems
Kybernetika, Tome 59 (2023) no. 3, pp. 392-417.

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In this paper, we design a distributed penalty ADMM algorithm with quantized communication to solve distributed convex optimization problems over multi-agent systems. Firstly, we introduce a quantization scheme that reduces the bandwidth limitation of multi-agent systems without requiring an encoder or decoder, unlike existing quantized algorithms. This scheme also minimizes the computation burden. Moreover, with the aid of the quantization design, we propose a quantized penalty ADMM to obtain the suboptimal solution. Furthermore, the proposed algorithm converges to the suboptimal solution with an $O(\frac{1}{k})$ convergence rate for general convex objective functions, and with an R-linear rate for strongly convex objective functions.
DOI : 10.14736/kyb-2023-3-0392
Classification : 90C33
Keywords: quantized communication; distributed optimization; alternating direction method of multipliers (ADMM); constrained optimization 
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     title = {A penalty {ADMM} with quantized communication for distributed optimization over multi-agent systems},
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Liu, Chenyang; Dou, Xiaohua; Fan, Yuan; Cheng, Songsong. A penalty ADMM with quantized communication for distributed optimization over multi-agent systems. Kybernetika, Tome 59 (2023) no. 3, pp. 392-417. doi : 10.14736/kyb-2023-3-0392. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2023-3-0392/

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