Discrete approximations for strict convex continuous time problems and duality

Detalhes bibliográficos
Autor(a) principal: Andreani, R.
Data de Publicação: 2004
Outros Autores: Goncalves, P. S. [UNESP], Silva, Geraldo Nunes [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://www.scielo.br/scielo.php?pid=S1807-03022004000100005&script=sci_arttext
http://hdl.handle.net/11449/34247
Resumo: We propose a discrete approximation scheme to a class of Linear Quadratic Continuous Time Problems. It is shown, under positiveness of the matrix in the integral cost, that optimal solutions of the discrete problems provide a sequence of bounded variation functions which converges almost everywhere to the unique optimal solution. Furthermore, the method of discretization allows us to derive a number of interesting results based on finite dimensional optimization theory, namely, Karush-Kuhn-Tucker conditions of optimality and weak and strong duality. A number of examples are provided to illustrate the theory.
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spelling Discrete approximations for strict convex continuous time problems and dualityLinear Quadratic problemsContinuous time optimizationdiscrete approximationstrict convexityWe propose a discrete approximation scheme to a class of Linear Quadratic Continuous Time Problems. It is shown, under positiveness of the matrix in the integral cost, that optimal solutions of the discrete problems provide a sequence of bounded variation functions which converges almost everywhere to the unique optimal solution. Furthermore, the method of discretization allows us to derive a number of interesting results based on finite dimensional optimization theory, namely, Karush-Kuhn-Tucker conditions of optimality and weak and strong duality. A number of examples are provided to illustrate the theory.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Univ Estadual Campinas, Dept Matemat Aplicada, IMECC, Campinas, SP, BrazilUniv Estadual Paulista, Sao Jose do Rio Preto, SP, BrazilUniv Estadual Paulista, Sao Jose do Rio Preto, SP, BrazilSoc Brasileira Matematica Aplicada & ComputacionalUniversidade Estadual de Campinas (UNICAMP)Universidade Estadual Paulista (Unesp)Andreani, R.Goncalves, P. S. [UNESP]Silva, Geraldo Nunes [UNESP]2014-05-20T15:23:28Z2014-05-20T15:23:28Z2004-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article81-105application/pdfhttp://www.scielo.br/scielo.php?pid=S1807-03022004000100005&script=sci_arttextComputational & Applied Mathematics. Sao Carlos Sp: Soc Brasileira Matematica Aplicada & Computacional, v. 23, n. 1, p. 81-105, 2004.0101-8205http://hdl.handle.net/11449/34247S1807-03022004000100005WOS:000208135000005WOS000208135000005.pdf3638688119433520Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengComputational & Applied Mathematics0.8630,272info:eu-repo/semantics/openAccess2023-11-14T06:15:35Zoai:repositorio.unesp.br:11449/34247Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T17:40:57.793690Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Discrete approximations for strict convex continuous time problems and duality
title Discrete approximations for strict convex continuous time problems and duality
spellingShingle Discrete approximations for strict convex continuous time problems and duality
Andreani, R.
Linear Quadratic problems
Continuous time optimization
discrete approximation
strict convexity
title_short Discrete approximations for strict convex continuous time problems and duality
title_full Discrete approximations for strict convex continuous time problems and duality
title_fullStr Discrete approximations for strict convex continuous time problems and duality
title_full_unstemmed Discrete approximations for strict convex continuous time problems and duality
title_sort Discrete approximations for strict convex continuous time problems and duality
author Andreani, R.
author_facet Andreani, R.
Goncalves, P. S. [UNESP]
Silva, Geraldo Nunes [UNESP]
author_role author
author2 Goncalves, P. S. [UNESP]
Silva, Geraldo Nunes [UNESP]
author2_role author
author
dc.contributor.none.fl_str_mv Universidade Estadual de Campinas (UNICAMP)
Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv Andreani, R.
Goncalves, P. S. [UNESP]
Silva, Geraldo Nunes [UNESP]
dc.subject.por.fl_str_mv Linear Quadratic problems
Continuous time optimization
discrete approximation
strict convexity
topic Linear Quadratic problems
Continuous time optimization
discrete approximation
strict convexity
description We propose a discrete approximation scheme to a class of Linear Quadratic Continuous Time Problems. It is shown, under positiveness of the matrix in the integral cost, that optimal solutions of the discrete problems provide a sequence of bounded variation functions which converges almost everywhere to the unique optimal solution. Furthermore, the method of discretization allows us to derive a number of interesting results based on finite dimensional optimization theory, namely, Karush-Kuhn-Tucker conditions of optimality and weak and strong duality. A number of examples are provided to illustrate the theory.
publishDate 2004
dc.date.none.fl_str_mv 2004-01-01
2014-05-20T15:23:28Z
2014-05-20T15:23:28Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://www.scielo.br/scielo.php?pid=S1807-03022004000100005&script=sci_arttext
Computational & Applied Mathematics. Sao Carlos Sp: Soc Brasileira Matematica Aplicada & Computacional, v. 23, n. 1, p. 81-105, 2004.
0101-8205
http://hdl.handle.net/11449/34247
S1807-03022004000100005
WOS:000208135000005
WOS000208135000005.pdf
3638688119433520
url http://www.scielo.br/scielo.php?pid=S1807-03022004000100005&script=sci_arttext
http://hdl.handle.net/11449/34247
identifier_str_mv Computational & Applied Mathematics. Sao Carlos Sp: Soc Brasileira Matematica Aplicada & Computacional, v. 23, n. 1, p. 81-105, 2004.
0101-8205
S1807-03022004000100005
WOS:000208135000005
WOS000208135000005.pdf
3638688119433520
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Computational & Applied Mathematics
0.863
0,272
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 81-105
application/pdf
dc.publisher.none.fl_str_mv Soc Brasileira Matematica Aplicada & Computacional
publisher.none.fl_str_mv Soc Brasileira Matematica Aplicada & Computacional
dc.source.none.fl_str_mv Web of Science
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_ 1808128844567150592

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