Lower-semicontinuity and optimization of convex functionals
Autor(a) principal: | |
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Data de Publicação: | 2009 |
Outros Autores: | |
Tipo de documento: | Artigo de conferência |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://www.ijpam.eu/contents/2009-51-2/5/5.pdf http://hdl.handle.net/11449/71430 |
Resumo: | The result that we treat in this article allows to the utilization of classic tools of convex analysis in the study of optimality conditions in the optimal control convex process for a Volterra-Stietjes linear integral equation in the Banach space G([a, b],X) of the regulated functions in [a, b], that is, the functions f : [a, 6] → X that have only descontinuity of first kind, in Dushnik (or interior) sense, and with an equality linear restriction. In this work we introduce a convex functional Lβf(x) of Nemytskii type, and we present conditions for its lower-semicontinuity. As consequence, Weierstrass Theorem garantees (under compacity conditions) the existence of solution to the problem min{Lβf(x)}. © 2009 Academic Publications. |
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Lower-semicontinuity and optimization of convex functionalsConvex optimizationRegulated functionsVolterra-Stietjes linear integral equationsThe result that we treat in this article allows to the utilization of classic tools of convex analysis in the study of optimality conditions in the optimal control convex process for a Volterra-Stietjes linear integral equation in the Banach space G([a, b],X) of the regulated functions in [a, b], that is, the functions f : [a, 6] → X that have only descontinuity of first kind, in Dushnik (or interior) sense, and with an equality linear restriction. In this work we introduce a convex functional Lβf(x) of Nemytskii type, and we present conditions for its lower-semicontinuity. As consequence, Weierstrass Theorem garantees (under compacity conditions) the existence of solution to the problem min{Lβf(x)}. © 2009 Academic Publications.Department of Mathematics UNESP-Ilha Solteira, Alameda Rio de Janeiro 266, 15385-000, Ilha Solteira, SPDepartment of Mathematics UNESP-Ilha Solteira, Alameda Rio de Janeiro 266, 15385-000, Ilha Solteira, SPUniversidade Estadual Paulista (Unesp)Fernandes, L. A O [UNESP]Arbach, R. [UNESP]2014-05-27T11:24:33Z2014-05-27T11:24:33Z2009-12-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/conferenceObject189-194application/pdfhttp://www.ijpam.eu/contents/2009-51-2/5/5.pdfInternational Journal of Pure and Applied Mathematics, v. 51, n. 2, p. 189-194, 2009.1311-8080http://hdl.handle.net/11449/714302-s2.0-786497733482-s2.0-78649773348.pdfScopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengInternational Journal of Pure and Applied Mathematics0,139info:eu-repo/semantics/openAccess2023-10-15T06:07:00Zoai:repositorio.unesp.br:11449/71430Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462023-10-15T06:07Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Lower-semicontinuity and optimization of convex functionals |
title |
Lower-semicontinuity and optimization of convex functionals |
spellingShingle |
Lower-semicontinuity and optimization of convex functionals Fernandes, L. A O [UNESP] Convex optimization Regulated functions Volterra-Stietjes linear integral equations |
title_short |
Lower-semicontinuity and optimization of convex functionals |
title_full |
Lower-semicontinuity and optimization of convex functionals |
title_fullStr |
Lower-semicontinuity and optimization of convex functionals |
title_full_unstemmed |
Lower-semicontinuity and optimization of convex functionals |
title_sort |
Lower-semicontinuity and optimization of convex functionals |
author |
Fernandes, L. A O [UNESP] |
author_facet |
Fernandes, L. A O [UNESP] Arbach, R. [UNESP] |
author_role |
author |
author2 |
Arbach, R. [UNESP] |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
Fernandes, L. A O [UNESP] Arbach, R. [UNESP] |
dc.subject.por.fl_str_mv |
Convex optimization Regulated functions Volterra-Stietjes linear integral equations |
topic |
Convex optimization Regulated functions Volterra-Stietjes linear integral equations |
description |
The result that we treat in this article allows to the utilization of classic tools of convex analysis in the study of optimality conditions in the optimal control convex process for a Volterra-Stietjes linear integral equation in the Banach space G([a, b],X) of the regulated functions in [a, b], that is, the functions f : [a, 6] → X that have only descontinuity of first kind, in Dushnik (or interior) sense, and with an equality linear restriction. In this work we introduce a convex functional Lβf(x) of Nemytskii type, and we present conditions for its lower-semicontinuity. As consequence, Weierstrass Theorem garantees (under compacity conditions) the existence of solution to the problem min{Lβf(x)}. © 2009 Academic Publications. |
publishDate |
2009 |
dc.date.none.fl_str_mv |
2009-12-01 2014-05-27T11:24:33Z 2014-05-27T11:24:33Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/conferenceObject |
format |
conferenceObject |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://www.ijpam.eu/contents/2009-51-2/5/5.pdf International Journal of Pure and Applied Mathematics, v. 51, n. 2, p. 189-194, 2009. 1311-8080 http://hdl.handle.net/11449/71430 2-s2.0-78649773348 2-s2.0-78649773348.pdf |
url |
http://www.ijpam.eu/contents/2009-51-2/5/5.pdf http://hdl.handle.net/11449/71430 |
identifier_str_mv |
International Journal of Pure and Applied Mathematics, v. 51, n. 2, p. 189-194, 2009. 1311-8080 2-s2.0-78649773348 2-s2.0-78649773348.pdf |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
International Journal of Pure and Applied Mathematics 0,139 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
189-194 application/pdf |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1799964572548857856 |