An nD-systems approach to global polynomial optimization with an application to H2 model order reduction

I.W.M. Bleylevens; R.L.M. Peeters; B. Hanzon

doi:10.1109/cdc.2005.1582972

An nD-systems approach to global polynomial optimization with an application to H2 model order reduction

I.W.M. Bleylevens^*
, R.L.M. Peeters
, B. Hanzon

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

Abstract

The problem of finding the global minimum of a multivariate polynomial can be approached by the matrix method of Stetter-Moller, which reformulates it as a large eigenvalue problem. The linear operators involved in this approach are studied using the theory of nD-systems. This supports the efficient application of iterative methods for solving eigenvalue problems such as Arnoldi methods and Jacobi-Davidson methods. This approach is demonstrated by an example which addresses optimal H2-model reduction of a linear dynamical model of order 10 to order 9. Index Terms: global polynomial optimization, Stetter-Moller matrix method, linear operator, nD-system, large eigenvalue problem, H2 model reduction

Original language	English
Title of host publication	Proceedings of CDC-ECC 2005
Subtitle of host publication	44th IEEE Conference on Decision and Control and European Control Conference 2005
Place of Publication	Sevilla
Publisher	IEEE
Pages	5107-5112
DOIs	https://doi.org/10.1109/cdc.2005.1582972
Publication status	Published - 1 Jan 2005
Event	44th IEEE Conference on Decision and Control and European Control Conference 2005 - Duration: 12 Dec 2005 → 15 Dec 2005

Conference

Conference	44th IEEE Conference on Decision and Control and European Control Conference 2005
Period	12/12/05 → 15/12/05

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10.1109/cdc.2005.1582972

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@inproceedings{c3976220e86b40bdb1b184982903fc35,

title = "An nD-systems approach to global polynomial optimization with an application to H2 model order reduction",

abstract = "The problem of finding the global minimum of a multivariate polynomial can be approached by the matrix method of Stetter-Moller, which reformulates it as a large eigenvalue problem. The linear operators involved in this approach are studied using the theory of nD-systems. This supports the efficient application of iterative methods for solving eigenvalue problems such as Arnoldi methods and Jacobi-Davidson methods. This approach is demonstrated by an example which addresses optimal H2-model reduction of a linear dynamical model of order 10 to order 9. Index Terms: global polynomial optimization, Stetter-Moller matrix method, linear operator, nD-system, large eigenvalue problem, H2 model reduction",

author = "I.W.M. Bleylevens and R.L.M. Peeters and B. Hanzon",

note = "Proceedings of CDC-ECC 2005: 44th IEEE Conference on Decision and Control and European Control Conference 2005 Sevilla ; 44th IEEE Conference on Decision and Control and European Control Conference 2005 ; Conference date: 12-12-2005 Through 15-12-2005",

year = "2005",

month = jan,

day = "1",

doi = "10.1109/cdc.2005.1582972",

language = "English",

pages = "5107--5112",

booktitle = "Proceedings of CDC-ECC 2005",

publisher = "IEEE",

address = "United States",

}

Bleylevens, IWM , Peeters, RLM & Hanzon, B 2005, An nD-systems approach to global polynomial optimization with an application to H2 model order reduction. in Proceedings of CDC-ECC 2005: 44th IEEE Conference on Decision and Control and European Control Conference 2005. IEEE, Sevilla, pp. 5107-5112, 44th IEEE Conference on Decision and Control and European Control Conference 2005, 12/12/05. https://doi.org/10.1109/cdc.2005.1582972

An nD-systems approach to global polynomial optimization with an application to H2 model order reduction. / Bleylevens, I.W.M.; Peeters, R.L.M.; Hanzon, B.
Proceedings of CDC-ECC 2005: 44th IEEE Conference on Decision and Control and European Control Conference 2005. Sevilla: IEEE, 2005. p. 5107-5112.

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

TY - GEN

T1 - An nD-systems approach to global polynomial optimization with an application to H2 model order reduction

AU - Bleylevens, I.W.M.

AU - Peeters, R.L.M.

AU - Hanzon, B.

N1 - Proceedings of CDC-ECC 2005: 44th IEEE Conference on Decision and Control and European Control Conference 2005 Sevilla

PY - 2005/1/1

Y1 - 2005/1/1

N2 - The problem of finding the global minimum of a multivariate polynomial can be approached by the matrix method of Stetter-Moller, which reformulates it as a large eigenvalue problem. The linear operators involved in this approach are studied using the theory of nD-systems. This supports the efficient application of iterative methods for solving eigenvalue problems such as Arnoldi methods and Jacobi-Davidson methods. This approach is demonstrated by an example which addresses optimal H2-model reduction of a linear dynamical model of order 10 to order 9. Index Terms: global polynomial optimization, Stetter-Moller matrix method, linear operator, nD-system, large eigenvalue problem, H2 model reduction

AB - The problem of finding the global minimum of a multivariate polynomial can be approached by the matrix method of Stetter-Moller, which reformulates it as a large eigenvalue problem. The linear operators involved in this approach are studied using the theory of nD-systems. This supports the efficient application of iterative methods for solving eigenvalue problems such as Arnoldi methods and Jacobi-Davidson methods. This approach is demonstrated by an example which addresses optimal H2-model reduction of a linear dynamical model of order 10 to order 9. Index Terms: global polynomial optimization, Stetter-Moller matrix method, linear operator, nD-system, large eigenvalue problem, H2 model reduction

U2 - 10.1109/cdc.2005.1582972

DO - 10.1109/cdc.2005.1582972

M3 - Conference article in proceeding

SP - 5107

EP - 5112

BT - Proceedings of CDC-ECC 2005

PB - IEEE

CY - Sevilla

T2 - 44th IEEE Conference on Decision and Control and European Control Conference 2005

Y2 - 12 December 2005 through 15 December 2005

ER -

An nD-systems approach to global polynomial optimization with an application to H2 model order reduction

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