Regularization Paths for Re-Weighted Nuclear Norm Minimization
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
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.
Re-weighted hankel matrix nuclear norm minimization, regularization path, weighted H-2 model reduction
Electrical Engineering, Electronic Engineering, Information Engineering
IdentifiersURN: urn:nbn:se:kth:diva-172469DOI: 10.1109/LSP.2015.2450505ISI: 000357620000007ScopusID: 2-s2.0-84960107877OAI: oai:DiVA.org:kth-172469DiVA: diva2:849040
FunderEU, European Research Council, 267381Swedish Research Council, 621-2009-4017
QC 201508272015-08-272015-08-252015-08-27Bibliographically approved