A non-classical class of variational problems

Detalhes bibliográficos
Autor(a) principal: João Pedro Cruz
Data de Publicação: 2010
Outros Autores: Delfim Torres, Alan S. I. Zinober
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/4454
Resumo: We study a new non-classical class of variational problems that is motivated by some recent research on the non-linear revenue problem in the field of economics. This class of problem can be set up as a maximising problem in the calculus of variations (CoV) or optimal control. However, the state value at the final fixed time, y(T), is a priori unknown and the integrand is a function of the unknown y(T). This is a non-standard CoV problem. In this paper we apply the new costate boundary conditions p(T) in the formulation of the CoV problem. We solve a sample example in this problem class using the numerical shooting method to solve the resulting TPBVP, and incorporate the free y(T) as an additional unknown. Essentially the same results are obtained using symbolic algebra software.
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spelling A non-classical class of variational problemsNon-linear revenue problemsTransversality conditionsCalculus of variationsShooting methodOptimal controlWe study a new non-classical class of variational problems that is motivated by some recent research on the non-linear revenue problem in the field of economics. This class of problem can be set up as a maximising problem in the calculus of variations (CoV) or optimal control. However, the state value at the final fixed time, y(T), is a priori unknown and the integrand is a function of the unknown y(T). This is a non-standard CoV problem. In this paper we apply the new costate boundary conditions p(T) in the formulation of the CoV problem. We solve a sample example in this problem class using the numerical shooting method to solve the resulting TPBVP, and incorporate the free y(T) as an additional unknown. Essentially the same results are obtained using symbolic algebra software.Inderscience2011-11-29T16:48:06Z2010-01-01T00:00:00Z2010info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/4454eng2040-3607João Pedro CruzDelfim TorresAlan S. I. Zinoberinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T11:05:05Zoai:ria.ua.pt:10773/4454Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:42:24.609838Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv A non-classical class of variational problems
title A non-classical class of variational problems
spellingShingle A non-classical class of variational problems
João Pedro Cruz
Non-linear revenue problems
Transversality conditions
Calculus of variations
Shooting method
Optimal control
title_short A non-classical class of variational problems
title_full A non-classical class of variational problems
title_fullStr A non-classical class of variational problems
title_full_unstemmed A non-classical class of variational problems
title_sort A non-classical class of variational problems
author João Pedro Cruz
author_facet João Pedro Cruz
Delfim Torres
Alan S. I. Zinober
author_role author
author2 Delfim Torres
Alan S. I. Zinober
author2_role author
author
dc.contributor.author.fl_str_mv João Pedro Cruz
Delfim Torres
Alan S. I. Zinober
dc.subject.por.fl_str_mv Non-linear revenue problems
Transversality conditions
Calculus of variations
Shooting method
Optimal control
topic Non-linear revenue problems
Transversality conditions
Calculus of variations
Shooting method
Optimal control
description We study a new non-classical class of variational problems that is motivated by some recent research on the non-linear revenue problem in the field of economics. This class of problem can be set up as a maximising problem in the calculus of variations (CoV) or optimal control. However, the state value at the final fixed time, y(T), is a priori unknown and the integrand is a function of the unknown y(T). This is a non-standard CoV problem. In this paper we apply the new costate boundary conditions p(T) in the formulation of the CoV problem. We solve a sample example in this problem class using the numerical shooting method to solve the resulting TPBVP, and incorporate the free y(T) as an additional unknown. Essentially the same results are obtained using symbolic algebra software.
publishDate 2010
dc.date.none.fl_str_mv 2010-01-01T00:00:00Z
2010
2011-11-29T16:48:06Z
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://hdl.handle.net/10773/4454
url http://hdl.handle.net/10773/4454
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 2040-3607
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Inderscience
publisher.none.fl_str_mv Inderscience
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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