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Approximate Regularization Paths for Nuclear Norm Minimization using Singular Value Bounds: with Implementation and Extended Appendix
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. (Systemidentifiering)ORCID iD: 0000-0002-4977-1055
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. (Systemidentifiering)ORCID iD: 0000-0003-0355-2663
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. (Systemidentifiering)ORCID iD: 0000-0002-1927-1690
2015 (English)Conference paper, Published paper (Refereed)
Abstract [en]

The widely used nuclear norm heuristic for rank minimizationproblems introduces a regularization parameter which isdifficult to tune. We have recently proposed a method to approximatethe regularization path, i.e., the optimal solution asa function of the parameter, which requires solving the problemonly for a sparse set of points. In this paper, we extendthe algorithm to provide error bounds for the singular valuesof the approximation. We exemplify the algorithms on largescale benchmark examples in model order reduction. Here,the order of a dynamical system is reduced by means of constrainedminimization of the nuclear norm of a Hankel matrix.

Place, publisher, year, edition, pages
2015.
National Category
Control Engineering Signal Processing
Identifiers
URN: urn:nbn:se:kth:diva-181804ISI: 000380425300034Scopus ID: 2-s2.0-84964054417OAI: oai:DiVA.org:kth-181804DiVA: diva2:900590
Conference
Signal Processing Education Workshop
Funder
EU, European Research CouncilSwedish Research Council, 621-2009-401
Note

QC 20160303

Available from: 2016-02-04 Created: 2016-02-04 Last updated: 2017-06-15Bibliographically approved

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fulltext(973 kB)26 downloads
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