Decentralized Proximal Gradient Algorithms With Linear Convergence Rates

This article studies a class of nonsmooth decentralized multiagent optimization problems where the agents aim at minimizing a sum of local strongly-convex smooth components plus a common nonsmooth term. We propose a general primal-dual algorithmic framework that unifies many existing state-of-the-ar...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 66; no. 6; pp. 2787 - 2794
Main Authors: Alghunaim, Sulaiman A., Ryu, Ernest K., Yuan, Kun, Sayed, Ali H.
Format: Journal Article
Language:English
Published: New York IEEE 01.06.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Approximation algorithms
Convergence
Convex functions
Cost function
Decentralized optimization
diffusion
Electronic mail
gradient tracking
linear convergence
Multiagent systems
Optimization
proximal gradient algorithms
Symmetric matrices
unified decentralized algorithm
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Summary:This article studies a class of nonsmooth decentralized multiagent optimization problems where the agents aim at minimizing a sum of local strongly-convex smooth components plus a common nonsmooth term. We propose a general primal-dual algorithmic framework that unifies many existing state-of-the-art algorithms. We establish linear convergence of the proposed method to the exact minimizer in the presence of the nonsmooth term. Moreover, for the more general class of problems with agent specific nonsmooth terms, we show that linear convergence cannot be achieved (in the worst case) for the class of algorithms that uses the gradients and the proximal mappings of the smooth and nonsmooth parts, respectively. We further provide a numerical counterexample that shows how some state-of-the-art algorithms fail to converge linearly for strongly convex objectives and different local non smooth terms.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2020.3009363