Distributed Primal-Dual Splitting Algorithm for Multiblock Separable Optimization Problems

This article considers the distributed structured optimization problem of collaboratively minimizing the global objective function composed of the sum of local cost functions. Each local objective function involves a Lipschitz-differentiable convex function, a nonsmooth convex function, and a linear...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 67; no. 8; pp. 4264 - 4271
Main Authors: Li, Huaqing, Wu, Xiangzhao, Wang, Zheng, Huang, Tingwen
Format: Journal Article
Language:English
Published: New York IEEE 01.08.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Asynchronous algorithm
Convergence
Convex functions
Cost function
Couplings
Distributed algorithms
distributed optimization
Linear programming
Optimization
Parameters
primal–dual splitting algorithm
Simulation
Splitting
uncoordinated stepsizes
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Summary:This article considers the distributed structured optimization problem of collaboratively minimizing the global objective function composed of the sum of local cost functions. Each local objective function involves a Lipschitz-differentiable convex function, a nonsmooth convex function, and a linear composite nonsmooth convex function. For such problems, we derive the synchronous distributed primal-dual splitting (S-DPDS) algorithm with uncoordinated stepsizes. Meanwhile, we develop the asynchronous version of the algorithm in light of the randomized block-coordinate method (A-DPDS). Further, the convergence results show the relaxed range and concise form of the acceptable parameters, which indicates that the algorithms are conducive to the selection of parameters in practical applications. Finally, we demonstrate the efficiency of S-DPDS and A-DPDS algorithms by numerical experiments.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2021.3116116