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A Comparative Analysis of the Fast-Lipschitz Convergence Speed
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0001-9810-3478
2012 (English)In: 2012 IEEE 51st Annual Conference on Decision and Control (CDC), IEEE conference proceedings, 2012, 7464-7469 p.Conference paper, Published paper (Refereed)
Abstract [en]

Fast-Lipschitz optimization is a recently proposed framework useful for an important class of centralized and distributed optimization problems over peer-to-peer networks. The properties of Fast-Lipschitz problems allow to compute the solution without having to introduce Lagrange multipliers, as in most other methods. This is highly beneficial, since multipliers need to be communicated across the network and thus increase the communication complexity of solution algorithms. Although the convergence speed of Fast-Lipschitz optimization methods often outperforms Lagrangian methods in practice, there is not yet a theoretical analysis. This paper provides a fundamental step towards such an analysis. Sufficient conditions for superior convergence of the Fast-Lipschitz method are established. The results are illustrated by simple examples. It is concluded that optimization problems with quadratic cost functions and linear constraints are always better solved by Fast-Lipschitz optimization methods, provided that certain conditions hold on the eigenvalues of the Hessian of the cost function and constraints.

Place, publisher, year, edition, pages
IEEE conference proceedings, 2012. 7464-7469 p.
Series
IEEE Conference on Decision and Control. Proceedings, ISSN 0191-2216
Keyword [en]
Convergence, Eigenvalues and eigenfunctions, Equations, Pareto optimization, Peer to peer computing, Vectors
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:kth:diva-111851DOI: 10.1109/CDC.2012.6426117ISI: 000327200407111Scopus ID: 2-s2.0-84874240340ISBN: 978-1-4673-2064-1 (print)OAI: oai:DiVA.org:kth-111851DiVA: diva2:587408
Conference
51st IEEE Conference on Decision and Control, CDC 2012; Maui, HI; United States; 10 December 2012 through 13 December 2012
Note

QC 20130115

Available from: 2013-02-12 Created: 2013-01-14 Last updated: 2013-12-19Bibliographically approved

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