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The ADMM Algorithm for Distributed Quadratic Problems: Parameter Selection and Constraint Preconditioning
KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0003-1835-2963
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2016 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 64, no 2, 290-305 p.Article in journal (Refereed) PublishedText
Abstract [en]

This paper presents optimal parameter selection and preconditioning of the alternating direction method of multipliers (ADMM) algorithm for a class of distributed quadratic problems, which can be formulated as equality-constrained quadratic programming problems. The parameter selection focuses on the ADMM step-size and relaxation parameter, while the preconditioning corresponds to selecting the edge weights of the underlying communication graph. We optimize these parameters to yield the smallest convergence factor of the iterates. Explicit expressions are derived for the step-size and relaxation parameter, as well as for the corresponding convergence factor. Numerical simulations justify our results and highlight the benefits of optimal parameter selection and preconditioning for the ADMM algorithm.

Place, publisher, year, edition, pages
IEEE , 2016. Vol. 64, no 2, 290-305 p.
Keyword [en]
Distributed optimization, convergence rate, optimal step-size
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:kth:diva-180962DOI: 10.1109/TSP.2015.2480041ISI: 000367253400002OAI: oai:DiVA.org:kth-180962DiVA: diva2:898836
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QC 20160129

Available from: 2016-01-29 Created: 2016-01-26 Last updated: 2016-01-29Bibliographically approved

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Sandberg, HenrikJohansson, Mikael
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