Discrete approximations for strict convex continuous time problems and duality

Detalhes bibliográficos
Autor(a) principal: Andreani, R.
Data de Publicação: 2004
Outros Autores: Gonçalves, P. S. [UNESP], Silva, G. N. [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1590/s1807-03022004000100005
http://hdl.handle.net/11449/219774
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.
id UNSP_f97741e193a2f61e827db343080f5417
oai_identifier_str oai:repositorio.unesp.br:11449/219774
network_acronym_str UNSP
network_name_str Repositório Institucional da UNESP
repository_id_str 2946
spelling Discrete approximations for strict convex continuous time problems and dualityContinuous time optimizationDiscrete approximationLinear Quadratic problemsStrict 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)Departamento de Matemática Aplicada IMECC UNICAMPUniversidade de Estadual PaulistaUniversidade de Estadual PaulistaUniversidade Estadual de Campinas (UNICAMP)Universidade Estadual Paulista (UNESP)Andreani, R.Gonçalves, P. S. [UNESP]Silva, G. N. [UNESP]2022-04-28T18:57:23Z2022-04-28T18:57:23Z2004-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article81-105http://dx.doi.org/10.1590/s1807-03022004000100005Computational and Applied Mathematics, v. 23, n. 1, p. 81-105, 2004.1807-03022238-3603http://hdl.handle.net/11449/21977410.1590/s1807-030220040001000052-s2.0-84858172432Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengComputational and Applied Mathematicsinfo:eu-repo/semantics/openAccess2022-04-28T18:57:23Zoai:repositorio.unesp.br:11449/219774Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T18:53:40.362816Repositório 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.
Continuous time optimization
Discrete approximation
Linear Quadratic problems
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.
Gonçalves, P. S. [UNESP]
Silva, G. N. [UNESP]
author_role author
author2 Gonçalves, P. S. [UNESP]
Silva, G. N. [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.
Gonçalves, P. S. [UNESP]
Silva, G. N. [UNESP]
dc.subject.por.fl_str_mv Continuous time optimization
Discrete approximation
Linear Quadratic problems
Strict convexity
topic Continuous time optimization
Discrete approximation
Linear Quadratic problems
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
2022-04-28T18:57:23Z
2022-04-28T18:57:23Z
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://dx.doi.org/10.1590/s1807-03022004000100005
Computational and Applied Mathematics, v. 23, n. 1, p. 81-105, 2004.
1807-0302
2238-3603
http://hdl.handle.net/11449/219774
10.1590/s1807-03022004000100005
2-s2.0-84858172432
url http://dx.doi.org/10.1590/s1807-03022004000100005
http://hdl.handle.net/11449/219774
identifier_str_mv Computational and Applied Mathematics, v. 23, n. 1, p. 81-105, 2004.
1807-0302
2238-3603
10.1590/s1807-03022004000100005
2-s2.0-84858172432
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Computational and Applied Mathematics
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 81-105
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_ 1808128996804657152

Registros relacionados