D-DistADMM: A O(1/k) Distributed ADMM for Distributed Optimization in Directed Graph Topologies

Vivek Khatana, Murti V. Salapaka

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

Abstract

We focus on the problem of minimizing a finite sum f(x) = \sum\nolimits_{i = 1}^n {{f_i}(x)} of n functions fi, where fi are convex and available only locally to an agent i. The n agents are connected in a directed network \mathcal{G} (V, E). In this article, we present the Directed-Distributed Alternating Direction Method of Multiplier (D-DistADMM) Algorithm, which is an Alternating Direction Method of Multiplier (ADMM) based scheme and utilizes a finite-time approximate consensus method to solve the above optimization problem distributively. At each iteration of the proposed scheme the agents solve their local optimization problem and utilize an approximate consensus protocol to update a local estimate of the global optimization variable. We show that for convex and not-necessarily differentiable objective functions the proposed D-DistADMM method converges at a rate O(1/k), where k is the iteration counter, in terms the difference between the Lagrangian function evaluated at any iteration k of the D-DistADMM algorithm and the optimal solution. We further demonstrate the features of our algorithm by solving a distributed least squares problem.

Original languageEnglish (US)
Title of host publication2020 59th IEEE Conference on Decision and Control, CDC 2020
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2992-2997
Number of pages6
ISBN (Electronic)9781728174471
DOIs
StatePublished - Dec 14 2020
Event59th IEEE Conference on Decision and Control, CDC 2020 - Virtual, Jeju Island, Korea, Republic of
Duration: Dec 14 2020Dec 18 2020

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2020-December
ISSN (Print)0743-1546

Conference

Conference59th IEEE Conference on Decision and Control, CDC 2020
CountryKorea, Republic of
CityVirtual, Jeju Island
Period12/14/2012/18/20

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.

Keywords

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

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