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Cited by 10Distributed Control Multi-Agent SystemsOptimization and Variational AnalysisAdvanced Optimization Algorithms Research

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Linear convergence rate for distributed optimization with the alternating direction method of multipliers

Iutzeler, F., Bianchi, P., Ciblat, Ph., Hachem, W.·2014·53rd IEEE Conference on Decision and Control
DOI 10.1109/cdc.2014.7040177
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Abstract

Consider the problem of distributed optimization where a network of N agents cooperate to solve a minimization problem of the form infxequation where function fnis convex and known only by agent n. The Alternating Direction Method of Multipliers (ADMM) has shown to be particularly efficient to solve this kind of problem. In this paper, we assume that there exists a unique minimum x*and that the functions fnare twice differentiable at x*and verify equation where the inequality is taken in the positive definite ordering. Under these assumptions, we prove the linear convergence of the distributed ADMM to the consensus over x*and derive a tight convergence rate. Finally, we give examples where one can derive the ADMM hyper-parameter ρ corresponding to the optimal rate.

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Research works printed but not linked: 25

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Metadata

Authors
Iutzeler, F., Bianchi, P., Ciblat, P., & Hachem, W.
Affiliations
  • Supélec (FR)
  • Centre National de la Recherche Scientifique (FR)
ORCID
Venue
53rd IEEE Conference on Decision and Control
Publisher
IEEE
Published
2014-12
Pages
5046-5051
ISSN
0191-2216 (ISSN-L)
DOI
10.1109/cdc.2014.7040177
OpenAlex
W2089969453
Cited by
10
References
0
Citations by year
2025: 1 · 2019: 1 · 2018: 2 · 2017: 3 · 2015: 3
FWCI
1.56
Type
conference paper
Language
en
Open access
closed
Locations
  • IEEE Conference on Decision and Control (CDC) (publishedVersion)
  • HAL (submittedVersion)
Topics
  • Physical Sciences › Engineering › Control and Systems Engineering › Distributed Control Multi-Agent Systems
  • Physical Sciences › Computer Science › Computational Theory and Mathematics › Optimization and Variational Analysis
  • Physical Sciences › Mathematics › Numerical Analysis › Advanced Optimization Algorithms Research
Keywords
distributed optimization, alternating direction method of multipliers, linear convergence, convergence rate, consensus, convex optimization, multi-agent systems, hyperparameter optimization, twice differentiable functions

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The paper
Iutzeler, F., Bianchi, P., Ciblat, P., & Hachem, W. (2014). Linear convergence rate for distributed optimization with the alternating direction method of multipliers. 53rd IEEE Conference on Decision and Control. https://doi.org/10.1109/cdc.2014.7040177