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Convergence of Limited Communications Gradient Methods
KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
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2016 (English)In: 2016 AMERICAN CONTROL CONFERENCE (ACC), IEEE conference proceedings, 2016, 1421-1426 p.Conference paper (Refereed)
Abstract [en]

Distributed control and decision making increasingly play a central role in economical and sustainable operation of cyber-physical systems. Nevertheless, the full potential of the technology has not yet been fully exploited in practice due to communication limitations of real-world infrastructures. This work investigates the fundamental properties of gradient methods for distributed optimization, where gradient information is communicated at every iteration, when using limited number of communicated bits. In particular, a general class of quantized gradient methods are studied where the gradient direction is approximated by a finite quantization set. Conditions on the quantization set are provided that are necessary and sufficient to guarantee the ability of these methods to minimize any convex objective function with Lipschitz continuous gradient and a nonempty, bounded set of optimizers. Moreover, a lower bound on the cardinality of the quantization set is provided, along with specific examples of minimal quantizations. Furthermore, convergence rate results are established that connect the fineness of the quantization and number of iterations needed to reach a predefined solution accuracy. The results provide a bound on the number of bits needed to achieve the desired accuracy. Finally, an application of the theory to resource allocation in power networks is demonstrated, and the theoretical results are substantiated by numerical simulations.

Place, publisher, year, edition, pages
IEEE conference proceedings, 2016. 1421-1426 p.
Series
Proceedings of the American Control Conference, ISSN 0743-1619
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:kth:diva-204146DOI: 10.1109/ACC.2016.7525116ISI: 000388376101076ScopusID: 2-s2.0-84992017454ISBN: 978-1-4673-8682-1 OAI: oai:DiVA.org:kth-204146DiVA: diva2:1084792
Conference
American Control Conference (ACC), JUL 06-08, 2016, Boston, MA
Note

QC 20170327

Available from: 2017-03-27 Created: 2017-03-27 Last updated: 2017-03-27Bibliographically approved

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Magnusson, SindriFischione, Carlo
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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf