Article
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Distributed Jacobi-Proximal ADMM for Consensus Convex Optimization
Version 1
: Received: 30 January 2024 / Approved: 31 January 2024 / Online: 31 January 2024 (12:58:05 CET)
How to cite: Xiao, X.-H.; Deng, H.; Xu, Y.-D. Distributed Jacobi-Proximal ADMM for Consensus Convex Optimization. Preprints 2024, 2024012201. https://doi.org/10.20944/preprints202401.2201.v1 Xiao, X.-H.; Deng, H.; Xu, Y.-D. Distributed Jacobi-Proximal ADMM for Consensus Convex Optimization. Preprints 2024, 2024012201. https://doi.org/10.20944/preprints202401.2201.v1
Abstract
In this paper, a distributed algorithm is proposed to solve a consensus convex optimization problem. It is a Jacobi-proximal alternating direction method of multipliers with a damping parameter $\gamma$ in the iteration of multiplier. Compared with existing algorithms, it has the following nice properties: (1) The restriction on proximal matrix is relaxed substantively, thus alleviating the weight of the proximal term. Therefore, the algorithm has a faster convergence speed. (2) The convergence analysis of the algorithm is established for any damping parameter $\gamma\in(0,2]$, which is larger ones in the literature. In addition, some numerical experiments and an application to a logistic regression problem are provided to validate the effectiveness and the characteristics of the proposed algorithm.
Keywords
Consensus convex optimization problem; Distributed Jacobi-proximal ADMM; Multi-agent system; Logistic regression
Subject
Computer Science and Mathematics, Computational Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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