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Article: Solving polynomial systems via LMI: Worst and best representation matrices

TitleSolving polynomial systems via LMI: Worst and best representation matrices
Authors
KeywordsConvex optimization
LMI
Polynomial system
Issue Date2009
PublisherCentre 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?
AbstractPolynomial 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 Identifierhttp://hdl.handle.net/10722/58851
ISSN
2015 SCImago Journal Rankings: 0.108
References

 

DC FieldValueLanguage
dc.contributor.authorChesi, Gen_HK
dc.date.accessioned2010-05-31T03:38:01Z-
dc.date.available2010-05-31T03:38:01Z-
dc.date.issued2009en_HK
dc.identifier.citationInternational Journal Of Applied Mathematics And Statistics, 2009, v. 14 J09, p. 47-59en_HK
dc.identifier.issn0973-1377en_HK
dc.identifier.urihttp://hdl.handle.net/10722/58851-
dc.description.abstractPolynomial 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.languageengen_HK
dc.publisherCentre 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.ispartofInternational Journal of Applied Mathematics and Statisticsen_HK
dc.subjectConvex optimizationen_HK
dc.subjectLMIen_HK
dc.subjectPolynomial systemen_HK
dc.titleSolving polynomial systems via LMI: Worst and best representation matricesen_HK
dc.typeArticleen_HK
dc.identifier.emailChesi, G:chesi@eee.hku.hken_HK
dc.identifier.authorityChesi, G=rp00100en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.scopuseid_2-s2.0-77954782016en_HK
dc.identifier.hkuros156190en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-77954782016&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume14en_HK
dc.identifier.issueJ09en_HK
dc.identifier.spage47en_HK
dc.identifier.epage59en_HK
dc.publisher.placeIndia-
dc.identifier.scopusauthoridChesi, G=7006328614en_HK

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