A geometrically convergent method for distributed optimization over time-varying graphs

Angelia Nedich, Alex Olshevsky, Wei Shi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Citations (Scopus)

Abstract

This paper considers the problem of distributed optimization over time-varying undirected graphs. We discuss a distributed algorithm, which we call DIGing, for solving this problem based on a combination of an inexact gradient method and a gradient tracking technique. This algorithm deploys fixed step size but converges exactly to the global and consensual minimizer. Under strong convexity assumption, we prove that the algorithm converges at an R-linear (geometric) convergence rate as long as the step size is less than a specific bound; we give an explicit estimate of this rate over uniformly connected graph sequences and show it scales polynomially with the number of nodes. Numerical experiments demonstrate the efficacy of the introduced algorithm and validate our theoretical findings.

Original languageEnglish (US)
Title of host publication2016 IEEE 55th Conference on Decision and Control, CDC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1023-1029
Number of pages7
ISBN (Electronic)9781509018376
DOIs
StatePublished - Dec 27 2016
Externally publishedYes
Event55th IEEE Conference on Decision and Control, CDC 2016 - Las Vegas, United States
Duration: Dec 12 2016Dec 14 2016

Other

Other55th IEEE Conference on Decision and Control, CDC 2016
CountryUnited States
CityLas Vegas
Period12/12/1612/14/16

Fingerprint

Distributed Optimization
Time-varying
Graph in graph theory
Geometric Convergence
Inexact Methods
Converge
Linear Convergence
Gradient methods
Gradient Method
Distributed Algorithms
Minimizer
Parallel algorithms
Undirected Graph
Convergence Rate
Convexity
Efficacy
Connected graph
Numerical Experiment
Gradient
Vertex of a graph

ASJC Scopus subject areas

  • Artificial Intelligence
  • Decision Sciences (miscellaneous)
  • Control and Optimization

Cite this

Nedich, A., Olshevsky, A., & Shi, W. (2016). A geometrically convergent method for distributed optimization over time-varying graphs. In 2016 IEEE 55th Conference on Decision and Control, CDC 2016 (pp. 1023-1029). [7798402] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2016.7798402

A geometrically convergent method for distributed optimization over time-varying graphs. / Nedich, Angelia; Olshevsky, Alex; Shi, Wei.

2016 IEEE 55th Conference on Decision and Control, CDC 2016. Institute of Electrical and Electronics Engineers Inc., 2016. p. 1023-1029 7798402.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Nedich, A, Olshevsky, A & Shi, W 2016, A geometrically convergent method for distributed optimization over time-varying graphs. in 2016 IEEE 55th Conference on Decision and Control, CDC 2016., 7798402, Institute of Electrical and Electronics Engineers Inc., pp. 1023-1029, 55th IEEE Conference on Decision and Control, CDC 2016, Las Vegas, United States, 12/12/16. https://doi.org/10.1109/CDC.2016.7798402
Nedich A, Olshevsky A, Shi W. A geometrically convergent method for distributed optimization over time-varying graphs. In 2016 IEEE 55th Conference on Decision and Control, CDC 2016. Institute of Electrical and Electronics Engineers Inc. 2016. p. 1023-1029. 7798402 https://doi.org/10.1109/CDC.2016.7798402
Nedich, Angelia ; Olshevsky, Alex ; Shi, Wei. / A geometrically convergent method for distributed optimization over time-varying graphs. 2016 IEEE 55th Conference on Decision and Control, CDC 2016. Institute of Electrical and Electronics Engineers Inc., 2016. pp. 1023-1029
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