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Regularization Paths for Re-Weighted Nuclear Norm Minimization
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0002-4977-1055
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0003-0355-2663
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0002-1927-1690
2015 (English)In: IEEE Signal Processing Letters, ISSN 1070-9908, E-ISSN 1558-2361, Vol. 22, no 11, 1980-1984 p.Article in journal (Refereed) Published
Abstract [en]

We consider a class of weighted nuclear norm optimization problems with important applications in signal processing, system identification, and model order reduction. The nuclear norm is commonly used as a convex heuristic for matrix rank constraints. Our objective is to minimize a quadratic cost subject to a nuclear norm constraint on a linear function of the decision variables, where the trade-off between the fit and the constraint is governed by a regularization parameter. The main contribution is an algorithm to determine the so-called approximate regularization path, which is the optimal solution up to a given error tolerance as a function of the regularization parameter. The advantage is that we only have to solve the optimization problem for a fixed number of values of the regularization parameter, with guaranteed error tolerance. The algorithm is exemplified on a weighted Hankel matrix model order reduction problem.

Place, publisher, year, edition, pages
2015. Vol. 22, no 11, 1980-1984 p.
Keyword [en]
Re-weighted hankel matrix nuclear norm minimization, regularization path, weighted H-2 model reduction
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:kth:diva-172469DOI: 10.1109/LSP.2015.2450505ISI: 000357620000007Scopus ID: 2-s2.0-84960107877OAI: oai:DiVA.org:kth-172469DiVA: diva2:849040
Funder
EU, European Research Council, 267381Swedish Research Council, 621-2009-4017
Note

QC 20150827

Available from: 2015-08-27 Created: 2015-08-25 Last updated: 2017-12-04Bibliographically approved

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Blomberg, NiclasRojas, Cristian R.Wahlberg, Bo

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