A fixed step distributed proximal gradient push‐pull algorithm based on integral quadratic constraint

In order to solve the distributed optimization problem with smooth + nonsmooth structure of the objective function on unbalanced directed networks, this article uses the proximal operator to deal with the nonsmooth part of the objective function, and designs and analyzes the fixed step proximal grad...

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Bibliographic Details
Published in:Optimal control applications & methods Vol. 44; no. 5; pp. 2693 - 2707
Main Authors: Gao, Wenhua, Xie, Yibin, Ren, Hongwei
Format: Journal Article
Language:English
Published: Glasgow Wiley Subscription Services, Inc 01.09.2023
Subjects:
Algorithms
Convergence
Linear matrix inequalities
Linear programming
Mathematical analysis
Operators (mathematics)
Optimization
Upper bounds
ISSN:0143-2087, 1099-1514
Online Access:Get full text
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Summary:In order to solve the distributed optimization problem with smooth + nonsmooth structure of the objective function on unbalanced directed networks, this article uses the proximal operator to deal with the nonsmooth part of the objective function, and designs and analyzes the fixed step proximal gradient Push‐Pull (PG‐Push‐Pull) algorithm. Firstly, the Integral Quadratic Constraint (IQC) suitable for proximal gradient Push‐Pull algorithm is given. When the smooth part of the objective function is strongly convex and the gradient satisfies the Lipchitz condition, the convergence of the algorithm is proved, and the convergence analysis is transformed into solving a linear matrix inequality by using this IQC framework. Its feasibility can ensure that the proposed algorithm has linear convergence rate, which is the same as that of Push‐Pull gradient algorithm. Then, the upper bound of convergence rate can be found by solving a Non‐Linear Programming problem. Finally, an example is given to analyze the upper bound of the convergence rate and verify the effectiveness of the proposed algorithm.
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ISSN:0143-2087
1099-1514
DOI:10.1002/oca.3000