DN-ADMM: Distributed Newton ADMM for Multi-agent Optimization

Yichuan Li, Nikolaos M. Freris, Petros Voulgaris, Dusan Stipanovic

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


In a multi-agent network, we consider the problem of minimizing an objective function that is expressed as the sum of private convex and smooth functions, and a (possibly) non-differentiable convex regularizer. We propose a novel distributed second-order method based on the framework of Alternating Direction Method of Multipliers (ADMM), by invoking approximate Newton iterations to the primal update corresponding to the differentiable part. In order to achieve a distributed implementation, the total Hessian matrix is split into a diagonal component (locally computable) and an off-diagonal component (that requires communication between neighboring agents). Subsequently, the Hessian inverse is approximated by a truncation of the Taylor expansion to K terms: this amounts to fully distributed updates entailing K distributed communication rounds. We establish global linear convergence to the primal-dual optimal solution under the assumption that the private functions are strongly convex and have Lipschitz continuous gradient. Numerical experiments demonstrate the merits of the approach comparatively with state-of-the-art methods.

Original languageEnglish (US)
Title of host publication60th IEEE Conference on Decision and Control, CDC 2021
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781665436595
StatePublished - 2021
Event60th IEEE Conference on Decision and Control, CDC 2021 - Austin, United States
Duration: Dec 13 2021Dec 17 2021

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370


Conference60th IEEE Conference on Decision and Control, CDC 2021
Country/TerritoryUnited States

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization


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