Theoretical and numerical results for some bi-objective optimal control problems

This article deals with the solution of some multi-objective optimal control problems for several PDEs: linear and semilinear elliptic equations and stationary Navier-Stokes systems. More precisely, we look for Pareto equilibria associated to standard cost functionals. First, we study the linear and...

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Detalles Bibliográficos
Autores: Fernández Cara, Enrique, Marín Gayte, Irene
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2019
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/167728
Acceso en línea:https://hdl.handle.net/11441/167728
https://doi.org/10.3934/cpaa.2020093
Access Level:acceso abierto
Palabra clave:Elliptic PDEs
Navier-Stokes equations
optimal control
bi-objective problems
Pareto equilibria
Dubovitskii-Milyutin formalism
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spelling Theoretical and numerical results for some bi-objective optimal control problemsFernández Cara, EnriqueMarín Gayte, IreneElliptic PDEsNavier-Stokes equationsoptimal controlbi-objective problemsPareto equilibriaDubovitskii-Milyutin formalismThis article deals with the solution of some multi-objective optimal control problems for several PDEs: linear and semilinear elliptic equations and stationary Navier-Stokes systems. More precisely, we look for Pareto equilibria associated to standard cost functionals. First, we study the linear and semilinear cases. We prove the existence of equilibria, we deduce appropriate optimality systems, we present some iterative algorithms and we establish convergence results. Then, we analyze the existence and characterization of Pareto equilibria for the Navier-Stokes equations. Here, we use the formalism of Dubovitskii and Milyutin. In this framework, we also present a finite element approximation of the bi-objective problem and we illustrate the techniques with several numerical experiments.AIMSEcuaciones Diferenciales y Análisis NuméricoFQM131: Ec.diferenciales,Simulacion Num.y Desarrollo Software2019info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/167728https://doi.org/10.3934/cpaa.2020093reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésCommunications on pure and Applied analysis, 19 (4), 2101-2126.https://dx.doi.org/10.3934/cpaa.2020093info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1677282026-06-17T12:51:07Z
dc.title.none.fl_str_mv Theoretical and numerical results for some bi-objective optimal control problems
title Theoretical and numerical results for some bi-objective optimal control problems
spellingShingle Theoretical and numerical results for some bi-objective optimal control problems
Fernández Cara, Enrique
Elliptic PDEs
Navier-Stokes equations
optimal control
bi-objective problems
Pareto equilibria
Dubovitskii-Milyutin formalism
title_short Theoretical and numerical results for some bi-objective optimal control problems
title_full Theoretical and numerical results for some bi-objective optimal control problems
title_fullStr Theoretical and numerical results for some bi-objective optimal control problems
title_full_unstemmed Theoretical and numerical results for some bi-objective optimal control problems
title_sort Theoretical and numerical results for some bi-objective optimal control problems
dc.creator.none.fl_str_mv Fernández Cara, Enrique
Marín Gayte, Irene
author Fernández Cara, Enrique
author_facet Fernández Cara, Enrique
Marín Gayte, Irene
author_role author
author2 Marín Gayte, Irene
author2_role author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
FQM131: Ec.diferenciales,Simulacion Num.y Desarrollo Software
dc.subject.none.fl_str_mv Elliptic PDEs
Navier-Stokes equations
optimal control
bi-objective problems
Pareto equilibria
Dubovitskii-Milyutin formalism
topic Elliptic PDEs
Navier-Stokes equations
optimal control
bi-objective problems
Pareto equilibria
Dubovitskii-Milyutin formalism
description This article deals with the solution of some multi-objective optimal control problems for several PDEs: linear and semilinear elliptic equations and stationary Navier-Stokes systems. More precisely, we look for Pareto equilibria associated to standard cost functionals. First, we study the linear and semilinear cases. We prove the existence of equilibria, we deduce appropriate optimality systems, we present some iterative algorithms and we establish convergence results. Then, we analyze the existence and characterization of Pareto equilibria for the Navier-Stokes equations. Here, we use the formalism of Dubovitskii and Milyutin. In this framework, we also present a finite element approximation of the bi-objective problem and we illustrate the techniques with several numerical experiments.
publishDate 2019
dc.date.none.fl_str_mv 2019
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/167728
https://doi.org/10.3934/cpaa.2020093
url https://hdl.handle.net/11441/167728
https://doi.org/10.3934/cpaa.2020093
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Communications on pure and Applied analysis, 19 (4), 2101-2126.
https://dx.doi.org/10.3934/cpaa.2020093
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv AIMS
publisher.none.fl_str_mv AIMS
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.812429

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