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Approximate regularization paths for nuclear norm minimization using singular value bounds
KTH, School of Electrical Engineering (EES), Automatic Control.
KTH, School of Electrical Engineering (EES), Automatic Control.ORCID iD: 0000-0003-0355-2663
KTH, School of Electrical Engineering (EES), Automatic Control.ORCID iD: 0000-0002-1927-1690
2015 (English)In: 2015 IEEE Signal Processing and Signal Processing Education Workshop, SP/SPE 2015, 2015, 190-195 p.Conference paper (Refereed)Text
Abstract [en]

The widely used nuclear norm heuristic for rank minimization problems introduces a regularization parameter which is difficult to tune. We have recently proposed a method to approximate the regularization path, i.e., the optimal solution as a function of the parameter, which requires solving the problem only for a sparse set of points. In this paper, we extend the algorithm to provide error bounds for the singular values of the approximation. We exemplify the algorithms on large scale benchmark examples in model order reduction. Here, the order of a dynamical system is reduced by means of constrained minimization of the nuclear norm of a Hankel matrix.

Place, publisher, year, edition, pages
2015. 190-195 p.
Keyword [en]
model order reduction, Nuclear norm heuristic, regularization path, singular value perturbation, Approximation algorithms, Constrained optimization, Dynamical systems, Error analysis, Matrix algebra, Constrained minimization, Nuclear norm minimizations, Rank minimizations, Regularization parameters, Regularization paths, Signal processing
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:kth:diva-186781DOI: 10.1109/DSP-SPE.2015.7369551ISI: 000380425300034ScopusID: 2-s2.0-84964054417ISBN: 9781467391696OAI: oai:DiVA.org:kth-186781DiVA: diva2:927951
Conference
IEEE Signal Processing and Signal Processing Education Workshop, SP/SPE 2015, 9 August 2015 through 12 August 2015
Note

QC 20160513

Available from: 2016-05-13 Created: 2016-05-13 Last updated: 2016-08-23Bibliographically approved

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Rojas, C. R.Wahlberg, Bo
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ReferencesLink to record
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