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Convergence of Limited Communications Gradient Methods
KTH, Skolan för elektro- och systemteknik (EES), Nätverk och systemteknik.ORCID-id: 0000-0002-6617-8683
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2016 (Engelska)Ingår i: 2016 American Control Conference (ACC), IEEE, 2016, s. 1421-1426Konferensbidrag, Publicerat paper (Refereegranskat)
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.

Ort, förlag, år, upplaga, sidor
IEEE, 2016. s. 1421-1426
Nationell ämneskategori
Reglerteknik
Forskningsämne
Elektro- och systemteknik
Identifikatorer
URN: urn:nbn:se:kth:diva-200474DOI: 10.1109/ACC.2016.7525116Scopus ID: 2-s2.0-84992017454OAI: oai:DiVA.org:kth-200474DiVA, id: diva2:1069117
Konferens
2016 American Control Conference (ACC)
Anmärkning

QC 20170201

Tillgänglig från: 2017-01-27 Skapad: 2017-01-27 Senast uppdaterad: 2018-12-04Bibliografiskt granskad

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Förlagets fulltextScopushttp://acc2016.a2c2.org/

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Fischione, Carlo

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Magnusson, SindriFischione, Carlo
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Nätverk och systemteknikACCESS Linnaeus Centre
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Totalt: 146 träffar
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