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Article: Solving polynomial systems via LMI: Worst and best representation matrices
Title | Solving polynomial systems via LMI: Worst and best representation matrices |
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Authors | |
Keywords | Convex optimization LMI Polynomial system |
Issue Date | 2009 |
Publisher | Centre for Environment, Social and Economic Research Publications. The Journal's web site is located at http://www.ceser.in/ceserp/index.php/ijamas |
Citation | International Journal Of Applied Mathematics And Statistics, 2009, v. 14 J09, p. 47-59 How to Cite? |
Abstract | Polynomial systems can be solved via LMI (linear matrix inequality) optimizations by exploiting the SMR (square matricial representation) of polynomials. This paper investigates the worst and best representation matrices obtainable in these LMI optimizations. In particular, it is shown that there always exist representation matrices for which the computation of the sought solutions either cannot be performed or is ill-conditioned. Moreover, it is shown that the best representation matrices for computing the sought solutions can be obtained by adding suitable LMIs, hence preserving the convexity of the optimization. © 2009 by IJAMAS, CESER. |
Persistent Identifier | http://hdl.handle.net/10722/58851 |
ISSN | 2023 Impact Factor: 0.3 |
References |
DC Field | Value | Language |
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dc.contributor.author | Chesi, G | en_HK |
dc.date.accessioned | 2010-05-31T03:38:01Z | - |
dc.date.available | 2010-05-31T03:38:01Z | - |
dc.date.issued | 2009 | en_HK |
dc.identifier.citation | International Journal Of Applied Mathematics And Statistics, 2009, v. 14 J09, p. 47-59 | en_HK |
dc.identifier.issn | 0973-1377 | en_HK |
dc.identifier.uri | http://hdl.handle.net/10722/58851 | - |
dc.description.abstract | Polynomial systems can be solved via LMI (linear matrix inequality) optimizations by exploiting the SMR (square matricial representation) of polynomials. This paper investigates the worst and best representation matrices obtainable in these LMI optimizations. In particular, it is shown that there always exist representation matrices for which the computation of the sought solutions either cannot be performed or is ill-conditioned. Moreover, it is shown that the best representation matrices for computing the sought solutions can be obtained by adding suitable LMIs, hence preserving the convexity of the optimization. © 2009 by IJAMAS, CESER. | en_HK |
dc.language | eng | en_HK |
dc.publisher | Centre for Environment, Social and Economic Research Publications. The Journal's web site is located at http://www.ceser.in/ceserp/index.php/ijamas | - |
dc.relation.ispartof | International Journal of Applied Mathematics and Statistics | en_HK |
dc.subject | Convex optimization | en_HK |
dc.subject | LMI | en_HK |
dc.subject | Polynomial system | en_HK |
dc.title | Solving polynomial systems via LMI: Worst and best representation matrices | en_HK |
dc.type | Article | en_HK |
dc.identifier.email | Chesi, G:chesi@eee.hku.hk | en_HK |
dc.identifier.authority | Chesi, G=rp00100 | en_HK |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.scopus | eid_2-s2.0-77954782016 | en_HK |
dc.identifier.hkuros | 156190 | en_HK |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-77954782016&selection=ref&src=s&origin=recordpage | en_HK |
dc.identifier.volume | 14 | en_HK |
dc.identifier.issue | J09 | en_HK |
dc.identifier.spage | 47 | en_HK |
dc.identifier.epage | 59 | en_HK |
dc.publisher.place | India | - |
dc.identifier.scopusauthorid | Chesi, G=7006328614 | en_HK |
dc.identifier.issnl | 0973-1377 | - |