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Article: An LMI approach to constrained optimization with homogeneous forms

TitleAn LMI approach to constrained optimization with homogeneous forms
Authors
KeywordsHomogeneous Form
Linear Matrix Inequalities (Lmis)
Optimization
Robustness
Stability
Issue Date2001
PublisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/sysconle
Citation
Systems And Control Letters, 2001, v. 42 n. 1, p. 11-19 How to Cite?
AbstractThis paper considers the problem of determining the minimum Euclidean distance of a point from a polynomial surface in Rn. It is well known that this problem is in general non-convex. The main purpose of the paper is to investigate to what extent linear matrix inequality (LMI) techniques can be exploited for solving this problem. The first result of the paper shows that a lower bound to the global minimum can be achieved via the solution of a one-parameter family of linear matrix inequalities (LMIs). It is also pointed out that for some classes of problems the solution of a single LMI problem provides the lower bound. The second result concerns the tightness of the bound. It is shown that optimality of the lower bound amounts to solving a system of linear equations. An application example is finally presented to show the features of the approach. © 2001 Elsevier Science B.V. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/155141
ISSN
2015 Impact Factor: 1.908
2015 SCImago Journal Rankings: 2.323
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorChesi, Gen_US
dc.contributor.authorTesi, Aen_US
dc.contributor.authorVicino, Aen_US
dc.contributor.authorGenesio, Ren_US
dc.date.accessioned2012-08-08T08:32:02Z-
dc.date.available2012-08-08T08:32:02Z-
dc.date.issued2001en_US
dc.identifier.citationSystems And Control Letters, 2001, v. 42 n. 1, p. 11-19en_US
dc.identifier.issn0167-6911en_US
dc.identifier.urihttp://hdl.handle.net/10722/155141-
dc.description.abstractThis paper considers the problem of determining the minimum Euclidean distance of a point from a polynomial surface in Rn. It is well known that this problem is in general non-convex. The main purpose of the paper is to investigate to what extent linear matrix inequality (LMI) techniques can be exploited for solving this problem. The first result of the paper shows that a lower bound to the global minimum can be achieved via the solution of a one-parameter family of linear matrix inequalities (LMIs). It is also pointed out that for some classes of problems the solution of a single LMI problem provides the lower bound. The second result concerns the tightness of the bound. It is shown that optimality of the lower bound amounts to solving a system of linear equations. An application example is finally presented to show the features of the approach. © 2001 Elsevier Science B.V. All rights reserved.en_US
dc.languageengen_US
dc.publisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/sysconleen_US
dc.relation.ispartofSystems and Control Lettersen_US
dc.subjectHomogeneous Formen_US
dc.subjectLinear Matrix Inequalities (Lmis)en_US
dc.subjectOptimizationen_US
dc.subjectRobustnessen_US
dc.subjectStabilityen_US
dc.titleAn LMI approach to constrained optimization with homogeneous formsen_US
dc.typeArticleen_US
dc.identifier.emailChesi, G:chesi@eee.hku.hken_US
dc.identifier.authorityChesi, G=rp00100en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1016/S0167-6911(00)00072-4en_US
dc.identifier.scopuseid_2-s2.0-0034899595en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0034899595&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume42en_US
dc.identifier.issue1en_US
dc.identifier.spage11en_US
dc.identifier.epage19en_US
dc.identifier.isiWOS:000166339800002-
dc.publisher.placeNetherlandsen_US
dc.identifier.scopusauthoridChesi, G=7006328614en_US
dc.identifier.scopusauthoridTesi, A=7007124648en_US
dc.identifier.scopusauthoridVicino, A=7006250298en_US
dc.identifier.scopusauthoridGenesio, R=7006875604en_US

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