State-constrained semilinear elliptic optimization problems with unrestricted sparse controls

In this paper, we consider optimal control problems associated with semilinear elliptic equation equations, where the states are subject to pointwise constraints but there are no explicit constraints on the controls. A term is included in the cost functional promoting the sparsity of the optimal con...

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Detalles Bibliográficos
Autores: Casas Rentería, Eduardo|||0000-0002-8364-9416, Tröltzsch, Fredi
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universidad de Cantabria (UC)
Repositorio:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:inglés
OAI Identifier:oai:repositorio.unican.es:10902/19006
Acceso en línea:http://hdl.handle.net/10902/19006
Access Level:acceso abierto
Palabra clave:Optimal control
Semilinear elliptic equations
First and second order optimality conditions
Sparse controls
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spelling State-constrained semilinear elliptic optimization problems with unrestricted sparse controlsCasas Rentería, Eduardo|||0000-0002-8364-9416Tröltzsch, FrediOptimal controlSemilinear elliptic equationsFirst and second order optimality conditionsSparse controlsIn this paper, we consider optimal control problems associated with semilinear elliptic equation equations, where the states are subject to pointwise constraints but there are no explicit constraints on the controls. A term is included in the cost functional promoting the sparsity of the optimal control. We prove existence of optimal controls and derive first and second order optimality conditions. In addition, we establish some regularity results for the optimal controls and the associated adjoint states and Lagrange multipliers.The first author was partially supported by Spanish Ministerio de Economía, Industria y Competitividad under projects MTM2014-57531-P and MTM2017-83185-P.American Institute of Mathematical SciencesUniversidad de Cantabria20202020-09-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articlehttp://hdl.handle.net/10902/19006Mathematical Control and Related Fields, 2020, 10(3), 527-546reponame:UCrea Repositorio Abierto de la Universidad de Cantabriainstname:Universidad de Cantabria (UC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:repositorio.unican.es:10902/190062026-06-02T12:39:31Z
dc.title.none.fl_str_mv State-constrained semilinear elliptic optimization problems with unrestricted sparse controls
title State-constrained semilinear elliptic optimization problems with unrestricted sparse controls
spellingShingle State-constrained semilinear elliptic optimization problems with unrestricted sparse controls
Casas Rentería, Eduardo|||0000-0002-8364-9416
Optimal control
Semilinear elliptic equations
First and second order optimality conditions
Sparse controls
title_short State-constrained semilinear elliptic optimization problems with unrestricted sparse controls
title_full State-constrained semilinear elliptic optimization problems with unrestricted sparse controls
title_fullStr State-constrained semilinear elliptic optimization problems with unrestricted sparse controls
title_full_unstemmed State-constrained semilinear elliptic optimization problems with unrestricted sparse controls
title_sort State-constrained semilinear elliptic optimization problems with unrestricted sparse controls
dc.creator.none.fl_str_mv Casas Rentería, Eduardo|||0000-0002-8364-9416
Tröltzsch, Fredi
author Casas Rentería, Eduardo|||0000-0002-8364-9416
author_facet Casas Rentería, Eduardo|||0000-0002-8364-9416
Tröltzsch, Fredi
author_role author
author2 Tröltzsch, Fredi
author2_role author
dc.contributor.none.fl_str_mv Universidad de Cantabria
dc.subject.none.fl_str_mv Optimal control
Semilinear elliptic equations
First and second order optimality conditions
Sparse controls
topic Optimal control
Semilinear elliptic equations
First and second order optimality conditions
Sparse controls
description In this paper, we consider optimal control problems associated with semilinear elliptic equation equations, where the states are subject to pointwise constraints but there are no explicit constraints on the controls. A term is included in the cost functional promoting the sparsity of the optimal control. We prove existence of optimal controls and derive first and second order optimality conditions. In addition, we establish some regularity results for the optimal controls and the associated adjoint states and Lagrange multipliers.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-09-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10902/19006
url http://hdl.handle.net/10902/19006
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv American Institute of Mathematical Sciences
publisher.none.fl_str_mv American Institute of Mathematical Sciences
dc.source.none.fl_str_mv Mathematical Control and Related Fields, 2020, 10(3), 527-546
reponame:UCrea Repositorio Abierto de la Universidad de Cantabria
instname:Universidad de Cantabria (UC)
instname_str Universidad de Cantabria (UC)
reponame_str UCrea Repositorio Abierto de la Universidad de Cantabria
collection UCrea Repositorio Abierto de la Universidad de Cantabria
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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