Asynchronous Distributed Nonsmooth Composite Optimization via Computation-Efficient Primal-Dual Proximal Algorithms

This paper focuses on a distributed nonsmooth composite optimization problem over a multiagent networked system, in which each agent is equipped with a local Lipschitz-differentiable function and two possibly nonsmooth functions, one of which incorporates a linear mapping. To address this problem, w...

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Vydané v:IEEE transactions on emerging topics in computational intelligence Ročník 9; číslo 2; s. 1595 - 1609
Hlavní autori: Ran, Liang, Li, Huaqing, Zheng, Lifeng, Li, Jun
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Piscataway IEEE 01.04.2025
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:
Algorithms
Asynchrony
Convergence
Convex functions
delayed communication
Delays
Distributed algorithms
distributed optimization algorithm
Multiagent systems
nonsmooth convex functions
Operators (mathematics)
Optimization
Vectors
ISSN:2471-285X, 2471-285X
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Shrnutí:This paper focuses on a distributed nonsmooth composite optimization problem over a multiagent networked system, in which each agent is equipped with a local Lipschitz-differentiable function and two possibly nonsmooth functions, one of which incorporates a linear mapping. To address this problem, we introduce a synchronous distributed algorithm featuring uncoordinated relaxed factors. It serves as a generalized relaxed version of the recent method TriPD-Dist. Notably, the considered problem in the presence of asynchrony and delays remains relatively unexplored. In response, a new asynchronous distributed primal-dual proximal algorithm is first proposed, rooted in a comprehensive asynchronous model. It is operated under the assumption that agents utilize possibly outdated information from their neighbors, while considering arbitrary, time-varying, yet bounded delays. With some special adjustments, new asynchronous distributed extensions of existing centralized methods are obtained via the proposed asynchronous algorithm. Theoretically, a new convergence analysis technique of the proposed algorithms is provided. Specifically, a sublinear convergence rate is explicitly derived by showcasing that the iteration behaves as a nonexpansive operator. In addition, the proposed asynchronous algorithm converges the optimal solution in expectation under the same step-size conditions as its synchronous counterpart. Finally, numerical studies substantiate the efficacy of the proposed algorithms and validate their performance in practical scenarios.
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ISSN:2471-285X
2471-285X
DOI:10.1109/TETCI.2024.3437249