An Asynchronous Approximate Distributed Alternating Direction Method of Multipliers in Digraphs

Wei Jiang, Andreas Grammenos, Evangelia Kalyvianaki, Themistoklis Charalambous

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

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Abstract

In this work, we consider the asynchronous distributed optimization problem in which each node has its own convex cost function and can communicate directly only with its neighbors, as determined by a directed communication topology (directed graph or digraph). First, we reformulate the optimization problem so that Alternating Direction Method of Multipliers (ADMM) can be utilized. Then, we propose an algorithm, herein called Asynchronous Approximate Distributed Alternating Direction Method of Multipliers (AsyAD-ADMM), using finite-time asynchronous approximate ratio consensus, to solve the multi-node convex optimization problem, in which every node performs iterative computations and exchanges information with its neighbors asynchronously. More specifically, at every iteration of AsyAD-ADMM, each node solves a local convex optimization problem for the one of the primal variables and utilizes a finite-time asynchronous approximate consensus protocol to obtain the value of the other variable which is close to the optimal value, since the cost function for the second primal variable is not decomposable. If the individual cost functions are convex, but not-necessarily differentiable, the proposed algorithm converges at a rate of O(1/k), where k is the iteration counter. The efficacy of AsyAD-ADMM is exemplified via a proof-of-concept distributed least square optimization problem with different performance-influencing factors investigated.

Original languageEnglish
Title of host publication60th IEEE Conference on Decision and Control, CDC 2021
PublisherIEEE
Pages3406-3413
Number of pages8
ISBN (Electronic)9781665436595
DOIs
Publication statusPublished - 2021
MoE publication typeA4 Article in a conference publication
EventIEEE Conference on Decision and Control - Austin, United States
Duration: 13 Dec 202117 Dec 2021
Conference number: 60

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2021-December
ISSN (Print)0743-1546

Conference

ConferenceIEEE Conference on Decision and Control
Abbreviated titleCDC
Country/TerritoryUnited States
CityAustin
Period13/12/202117/12/2021

Keywords

  • asynchronous ADMM
  • directed graphs
  • Distributed optimization
  • finite-time consensus
  • ratio consensus

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