A Distributed Proximal Alternating Direction Multiplier Method for Multiblock Nonsmooth Composite Optimization

In this article, we address a composite optimization problem in a distributed network. Each agent in the network possesses a private local convex function consisting of a differentiable term, a nonsmooth term, and a nonsmooth term combined with a linear operator. The objective is to minimize the sum...

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Published in:	IEEE transactions on control of network systems Vol. 12; no. 1; pp. 202 - 215
Main Authors:	Zhou, Yuan, Guo, Luyao, Shi, Xinli, Cao, Jinde
Format:	Journal Article
Language:	English
Published:	Piscataway IEEE 01.03.2025 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Algorithms Artificial neural networks Asynchronous algorithm Convergence Convex functions distributed composite optimization Linear operators Linear programming Machine learning algorithms Multipliers Network topologies Operators (mathematics) Optimization proximal alternating direction multiplier method (ADMM) Vectors
ISSN:	2325-5870, 2372-2533
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Abstract	In this article, we address a composite optimization problem in a distributed network. Each agent in the network possesses a private local convex function consisting of a differentiable term, a nonsmooth term, and a nonsmooth term combined with a linear operator. The objective is to minimize the sum of all local functions while achieving consensus among the local states through information exchange with neighboring agents. To tackle this problem, we propose a novel distributed proximal alternating direction multiplier method (ADMM). By introducing the proximal operator of the nonsmooth term, linearizing the smooth term, and incorporating an additional proximal term, the ADMM subproblem can be solved more efficiently. One key advantage of the proposed algorithm is that it allows each agent to select parameters without being constrained by the network topology. In some instances, the algorithm can be transformed into some classical optimization algorithms. The algorithm is further extended to an asynchronous version by introducing randomized block coordinate. We further analyze the convergence of the proposed asynchronous algorithm and establish the sublinear convergence rate under synchronous conditions. Finally, several numerical experiments are conducted to verify the effectiveness of the proposed algorithm.
AbstractList	In this article, we address a composite optimization problem in a distributed network. Each agent in the network possesses a private local convex function consisting of a differentiable term, a nonsmooth term, and a nonsmooth term combined with a linear operator. The objective is to minimize the sum of all local functions while achieving consensus among the local states through information exchange with neighboring agents. To tackle this problem, we propose a novel distributed proximal alternating direction multiplier method (ADMM). By introducing the proximal operator of the nonsmooth term, linearizing the smooth term, and incorporating an additional proximal term, the ADMM subproblem can be solved more efficiently. One key advantage of the proposed algorithm is that it allows each agent to select parameters without being constrained by the network topology. In some instances, the algorithm can be transformed into some classical optimization algorithms. The algorithm is further extended to an asynchronous version by introducing randomized block coordinate. We further analyze the convergence of the proposed asynchronous algorithm and establish the sublinear convergence rate under synchronous conditions. Finally, several numerical experiments are conducted to verify the effectiveness of the proposed algorithm.
Author	Cao, Jinde Guo, Luyao Shi, Xinli Zhou, Yuan
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SubjectTerms	Algorithms Artificial neural networks Asynchronous algorithm Convergence Convex functions distributed composite optimization Linear operators Linear programming Machine learning algorithms Multipliers Network topologies Operators (mathematics) Optimization proximal alternating direction multiplier method (ADMM) Vectors
Title	A Distributed Proximal Alternating Direction Multiplier Method for Multiblock Nonsmooth Composite Optimization
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