DocumentCode :
112667
Title :
Regularization Paths for Re-Weighted Nuclear Norm Minimization
Author :
Blomberg, Niclas ; Rojas, Cristian R. ; Wahlberg, Bo
Author_Institution :
Dept. of Autom. Control & ACCESS Linnaeus Center, KTH-R. Inst. of Technol., Stockholm, Sweden
Volume :
22
Issue :
11
fYear :
2015
fDate :
Nov. 2015
Firstpage :
1980
Lastpage :
1984
Abstract :
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.
Keywords :
Hankel matrices; minimisation; signal processing; matrix rank constraints; model order reduction; nuclear norm constraint; re-weigphted nuclear norm minimization; signal processing; system identification; weighted Hankel matrix model order reduction problem; weighted nuclear norm optimization problems; Approximation algorithms; Approximation error; Minimization; Optimization; Signal processing algorithms; Upper bound; Re-weighted hankel matrix nuclear norm minimization; regularization path; weighted ${H_2}$ model reduction;
fLanguage :
English
Journal_Title :
Signal Processing Letters, IEEE
Publisher :
ieee
ISSN :
1070-9908
Type :
jour
DOI :
10.1109/LSP.2015.2450505
Filename :
7138597
Link To Document :
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