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Fast-Lipschitz Optimization With Wireless Sensor Networks Applications
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0001-9810-3478
2011 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 56, no 10, 2319-2331 p.Article in journal (Refereed) Published
Abstract [en]

Motivated by the need for fast computations in wireless sensor networks, the new F-Lipschitz optimization theory is introduced for a novel class of optimization problems. These problems are defined by simple qualifying properties specified in terms of increasing objective function and contractive constraints. It is shown that feasible F-Lipschitz problems have always a unique optimal solution that satisfies the constraints at equality. The solution is obtained quickly by asynchronous algorithms of certified convergence. F-Lipschitz optimization can be applied to both centralized and distributed optimization. Compared to traditional Lagrangian methods, which often converge linearly, the convergence time of centralized F-Lipschitz problems is at least superlinear. Distributed F-Lipschitz algorithms converge fast, as opposed to traditional Lagrangian decomposition and parallelization methods, which generally converge slowly and at the price of many message passings. In both cases, the computational complexity is much lower than traditional Lagrangian methods. Examples of application of the new optimization method are given for distributed estimation and radio power control in wireless sensor networks. The drawback of the F-Lipschitz optimization is that it might be difficult to check the qualifying properties. For more general optimization problems, it is suggested that it is convenient to have conditions ensuring that the solution satisfies the constraints at equality.

Place, publisher, year, edition, pages
2011. Vol. 56, no 10, 2319-2331 p.
Keyword [en]
Convex and non-convex optimization, distributed optimization, interference function theory, multi-objective optimization, parallel and distributed computation, wireless sensor networks
National Category
Control Engineering
URN: urn:nbn:se:kth:diva-45590DOI: 10.1109/TAC.2011.2163855ISI: 000295581400007ScopusID: 2-s2.0-80053637184OAI: diva2:454264
Swedish Research CouncilTrenOp, Transport Research Environment with Novel PerspectivesICT - The Next Generation
QC 20111107Available from: 2011-11-07 Created: 2011-10-31 Last updated: 2012-06-13Bibliographically approved

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