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


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.
Number of pages6
ISBN (Electronic)9781538682661
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
ISSN (Print)0743-1619


Conference2020 American Control Conference, ACC 2020
Country/TerritoryUnited States

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.


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


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