A non-classical class of variational problems
Autor(a) principal: | |
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Data de Publicação: | 2010 |
Outros Autores: | , |
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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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 |
instacron_str |
RCAAP |
institution |
RCAAP |
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 |
repository.mail.fl_str_mv |
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1799137472338198528 |