Gradient-Consensus Method for Distributed Optimization in Directed Multi-Agent Networks

Vivek Khatana, Govind Saraswat, Sourav Patel, Murti V. Salapaka

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

8 Scopus citations

Abstract

In this article, a distributed optimization problem for minimizing a sum, sum {-{i = 1}-n{f-i}} , of convex objective functions, fi, on directed graph topologies is addressed. Here each function fi is a function of n variables, private to agent i which defines the agent's objective. These fi's are assumed to be Lipschitz-differentiable convex functions. For solving this optimization problem, we develop a novel distributed algorithm, which we term as the gradient-consensus method. The gradient-consensus scheme uses a finite-time terminated consensus protocol called ρ-consensus, which allows each local estimate to be ρ-close to each other at every iteration. The parameter ρ is a fixed constant independent of the network size and topology. It is shown that the estimate of the optimal solution at any local agent i converges geometrically to the optimal solution within an O(ρ) neighborhood, where ρ can be chosen to be arbitrarily small.

Original languageEnglish (US)
Title of host publication2020 American Control Conference, ACC 2020
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4689-4694
Number of pages6
ISBN (Electronic)9781538682661
DOIs
StatePublished - Jul 2020
Event2020 American Control Conference, ACC 2020 - Denver, United States
Duration: Jul 1 2020Jul 3 2020

Publication series

NameProceedings of the American Control Conference
Volume2020-July
ISSN (Print)0743-1619

Conference

Conference2020 American Control Conference, ACC 2020
Country/TerritoryUnited States
CityDenver
Period7/1/207/3/20

Bibliographical note

Funding Information:
This work is supported by Advanced Research Projects Agency-Energy OPEN through the project titled "Rapidly Viable Sustained Grid" via grant no. DE-AR0001016.

Publisher Copyright:
© 2020 AACC.

Keywords

  • Distributed optimization
  • distributed gradient descent
  • finite-time consensus
  • multi-agent networks

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