Structured low-rank approximation as a rational function minimization

Konstantin Usevich; Ivan Markovsky

doi:10.3182/20120711-3-BE-2027.00143

Structured low-rank approximation as a rational function minimization

Konstantin Usevich, Ivan Markovsky

Electricity

Research output: Chapter in Book/Report/Conference proceeding › Conference paper

10 Citations (Scopus)

Abstract

Many problems of system identification, model reduction and signal processing can be posed and solved as a structured low-rank approximation problem. In this paper a reformulation of the structured low-rank approximation problem as minimization of a multivariate rational cost function is considered. We show that in two different parametrizations the problem is reduced to optimization on a compact manifold or to a set of optimization problems on bounded domains of Euclidean space. We make a review of polynomial algebra methods for global optimization of the rational cost function.

Original language	English
Title of host publication	Proceedings of the 16th IFAC Symposium on System Identification, Brussels, Belgium, July 11-13, 2012
Publisher	Elsevier
Pages	722-727
Number of pages	6
ISBN (Print)	978-3-902823-10-6
DOIs	https://doi.org/10.3182/20120711-3-BE-2027.00143
Publication status	Published - 11 Jul 2012
Event	16th IFAC Symposium on System Identification (Sysid 2012) - SQUARE Brussels Meeting Center, Brussels, Belgium Duration: 11 Jul 2012 → 13 Jul 2012 http://www.sysid2012.org

Publication series

Name	IFAC Proceedings Volumes
Publisher	Elsevier
Number	16
Volume	45
ISSN (Electronic)	2405-8963

Conference

Conference	16th IFAC Symposium on System Identification (Sysid 2012)
Abbreviated title	Sysid 2012
Country/Territory	Belgium
City	Brussels
Period	11/07/12 → 13/07/12
Other	The scope of the symposium covers all major aspects of system identification, experimental modelling, signal processing and adaptive control, ranging from theoretical, methodological and scientific developments to a large variety of application areas. To enhance the applications and industrial perspective of the symposium, participation by authors from industry is particularly encouraged. It is the intention of the organizers to promote SYSID 2012 as a meeting place where scientists and engineers from several research communities can meet to discuss issues related to these areas.
Internet address	http://www.sysid2012.org

Keywords

low-rank approximation

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@inproceedings{d759bd02397c4eecac12ef9f3bd58c7b,

title = "Structured low-rank approximation as a rational function minimization",

abstract = "Many problems of system identification, model reduction and signal processing can be posed and solved as a structured low-rank approximation problem. In this paper a reformulation of the structured low-rank approximation problem as minimization of a multivariate rational cost function is considered. We show that in two different parametrizations the problem is reduced to optimization on a compact manifold or to a set of optimization problems on bounded domains of Euclidean space. We make a review of polynomial algebra methods for global optimization of the rational cost function.",

keywords = "low-rank approximation",

author = "Konstantin Usevich and Ivan Markovsky",

year = "2012",

month = jul,

day = "11",

doi = "10.3182/20120711-3-BE-2027.00143",

language = "English",

isbn = "978-3-902823-10-6",

series = "IFAC Proceedings Volumes",

publisher = "Elsevier",

number = "16",

pages = "722--727",

booktitle = "Proceedings of the 16th IFAC Symposium on System Identification, Brussels, Belgium, July 11-13, 2012",

note = "16th IFAC Symposium on System Identification (Sysid 2012), Sysid 2012 ; Conference date: 11-07-2012 Through 13-07-2012",

url = "http://www.sysid2012.org",

}

Usevich, K & Markovsky, I 2012, Structured low-rank approximation as a rational function minimization. in Proceedings of the 16th IFAC Symposium on System Identification, Brussels, Belgium, July 11-13, 2012. IFAC Proceedings Volumes, no. 16, vol. 45, Elsevier, pp. 722-727, 16th IFAC Symposium on System Identification (Sysid 2012), Brussels, Belgium, 11/07/12. https://doi.org/10.3182/20120711-3-BE-2027.00143

TY - GEN

T1 - Structured low-rank approximation as a rational function minimization

AU - Usevich, Konstantin

AU - Markovsky, Ivan

PY - 2012/7/11

Y1 - 2012/7/11

N2 - Many problems of system identification, model reduction and signal processing can be posed and solved as a structured low-rank approximation problem. In this paper a reformulation of the structured low-rank approximation problem as minimization of a multivariate rational cost function is considered. We show that in two different parametrizations the problem is reduced to optimization on a compact manifold or to a set of optimization problems on bounded domains of Euclidean space. We make a review of polynomial algebra methods for global optimization of the rational cost function.

AB - Many problems of system identification, model reduction and signal processing can be posed and solved as a structured low-rank approximation problem. In this paper a reformulation of the structured low-rank approximation problem as minimization of a multivariate rational cost function is considered. We show that in two different parametrizations the problem is reduced to optimization on a compact manifold or to a set of optimization problems on bounded domains of Euclidean space. We make a review of polynomial algebra methods for global optimization of the rational cost function.

KW - low-rank approximation

U2 - 10.3182/20120711-3-BE-2027.00143

DO - 10.3182/20120711-3-BE-2027.00143

M3 - Conference paper

SN - 978-3-902823-10-6

T3 - IFAC Proceedings Volumes

SP - 722

EP - 727

BT - Proceedings of the 16th IFAC Symposium on System Identification, Brussels, Belgium, July 11-13, 2012

PB - Elsevier

T2 - 16th IFAC Symposium on System Identification (Sysid 2012)

Y2 - 11 July 2012 through 13 July 2012

ER -

Structured low-rank approximation as a rational function minimization

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Keywords

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