Distributed Discrete-Time Convex Optimization With Closed Convex Set Constraints: Linearly Convergent Algorithm Design

The convergence rate and applicability to directed graphs with interaction topologies are two important features for practical applications of distributed optimization algorithms. In this article, a new kind of fast distributed discrete-time algorithms is developed for solving convex optimization pr...

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Bibliographic Details
Published in:IEEE transactions on cybernetics Vol. 54; no. 4; pp. 2271 - 2283
Main Authors: Luan, Meng, Wen, Guanghui, Liu, Hongzhe, Huang, Tingwen, Chen, Guanrong, Yu, Wenwu
Format: Journal Article
Language:English
Published: United States IEEE 01.04.2024
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Computational geometry
Consensus
Consensus algorithm
Convergence
Convex functions
Convexity
directed interaction topology
distributed constrained optimization
Eigenvalues and eigenfunctions
gradient tracking
Graph theory
Graphs
linear convergence rate
Momentum
Network topology
Numerical simulation
Optimization
Topology
ISSN:2168-2267, 2168-2275, 2168-2275
Online Access:Get full text
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Summary:The convergence rate and applicability to directed graphs with interaction topologies are two important features for practical applications of distributed optimization algorithms. In this article, a new kind of fast distributed discrete-time algorithms is developed for solving convex optimization problems with closed convex set constraints over directed interaction networks. Under the gradient tracking framework, two distributed algorithms are, respectively, designed over balanced and unbalanced graphs, where momentum terms and two time-scales are involved. Furthermore, it is demonstrated that the designed distributed algorithms attain linear speedup convergence rates provided that the momentum coefficients and the step size are appropriately selected. Finally, numerical simulations verify the effectiveness and the global accelerated effect of the designed algorithms.
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ISSN:2168-2267
2168-2275
2168-2275
DOI:10.1109/TCYB.2023.3270185