State error estimates for the numerical approximation of sparse distributed control problems in the absence of Tikhonov regularization

In this paper, we analyze optimal control problems of semilinear elliptic equations, where the controls are distributed. Box constraints for the controls are imposed and the cost functional does not involve the control itself, except possibly for a non-differentiable sparsity-promoting term. Under a...

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Detalhes bibliográficos
Autores: Casas Rentería, Eduardo|||0000-0002-8364-9416, Mateos Alberdi, Mariano
Tipo de documento: artigo
Data de publicação:2021
País:España
Recursos:Universidad de Cantabria (UC)
Repositório:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:inglês
OAI Identifier:oai:repositorio.unican.es:10902/22738
Acesso em linha:http://hdl.handle.net/10902/22738
Access Level:Acceso aberto
Palavra-chave:Optimal control
Bang-bang controls
Semilinear elliptic equations
Optimality conditions
Error estimates
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spelling State error estimates for the numerical approximation of sparse distributed control problems in the absence of Tikhonov regularizationCasas Rentería, Eduardo|||0000-0002-8364-9416Mateos Alberdi, MarianoOptimal controlBang-bang controlsSemilinear elliptic equationsOptimality conditionsError estimatesIn this paper, we analyze optimal control problems of semilinear elliptic equations, where the controls are distributed. Box constraints for the controls are imposed and the cost functional does not involve the control itself, except possibly for a non-differentiable sparsity-promoting term. Under appropriate second order sufficient optimality conditions, first we estimate the difference between the dis crete and continuous optimal states. Next, under an additional assumption on the optimal adjoint state, we prove error estimates for the controls and improve the estimates for the states.The authors were partially supported by Spanish Ministerio de Economía y Competitividad under research project MTM2017-83185-P.Springer Science + Business MediaUniversidad de Cantabria20212021-09-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articlehttp://hdl.handle.net/10902/22738Vietnam Journal of Mathematics, 2021, 49(3), 713-738 - (CORRIGENDUM), 2023, 51(2), 565-566reponame: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:10902/227382026-06-02T12:39:31Z
dc.title.none.fl_str_mv State error estimates for the numerical approximation of sparse distributed control problems in the absence of Tikhonov regularization
title State error estimates for the numerical approximation of sparse distributed control problems in the absence of Tikhonov regularization
spellingShingle State error estimates for the numerical approximation of sparse distributed control problems in the absence of Tikhonov regularization
Casas Rentería, Eduardo|||0000-0002-8364-9416
Optimal control
Bang-bang controls
Semilinear elliptic equations
Optimality conditions
Error estimates
title_short State error estimates for the numerical approximation of sparse distributed control problems in the absence of Tikhonov regularization
title_full State error estimates for the numerical approximation of sparse distributed control problems in the absence of Tikhonov regularization
title_fullStr State error estimates for the numerical approximation of sparse distributed control problems in the absence of Tikhonov regularization
title_full_unstemmed State error estimates for the numerical approximation of sparse distributed control problems in the absence of Tikhonov regularization
title_sort State error estimates for the numerical approximation of sparse distributed control problems in the absence of Tikhonov regularization
dc.creator.none.fl_str_mv Casas Rentería, Eduardo|||0000-0002-8364-9416
Mateos Alberdi, Mariano
author Casas Rentería, Eduardo|||0000-0002-8364-9416
author_facet Casas Rentería, Eduardo|||0000-0002-8364-9416
Mateos Alberdi, Mariano
author_role author
author2 Mateos Alberdi, Mariano
author2_role author
dc.contributor.none.fl_str_mv Universidad de Cantabria
dc.subject.none.fl_str_mv Optimal control
Bang-bang controls
Semilinear elliptic equations
Optimality conditions
Error estimates
topic Optimal control
Bang-bang controls
Semilinear elliptic equations
Optimality conditions
Error estimates
description In this paper, we analyze optimal control problems of semilinear elliptic equations, where the controls are distributed. Box constraints for the controls are imposed and the cost functional does not involve the control itself, except possibly for a non-differentiable sparsity-promoting term. Under appropriate second order sufficient optimality conditions, first we estimate the difference between the dis crete and continuous optimal states. Next, under an additional assumption on the optimal adjoint state, we prove error estimates for the controls and improve the estimates for the states.
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-09-01
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/10902/22738
url http://hdl.handle.net/10902/22738
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 Springer Science + Business Media
publisher.none.fl_str_mv Springer Science + Business Media
dc.source.none.fl_str_mv Vietnam Journal of Mathematics, 2021, 49(3), 713-738 - (CORRIGENDUM), 2023, 51(2), 565-566
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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