Optimality conditions and error analysis of semilinear elliptic control problems with L1 cost functional

Semilinear elliptic optimal control problems involving the L1 norm of the control in the objective are considered. Necessary and sufficient second-order optimality conditions are derived. A priori finite element error estimates for piecewise constant discretizations for the control and piecewise lin...

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Autores: Casas Rentería, Eduardo|||0000-0002-8364-9416, Herzog, Roland, Wachsmuth, Gerd
Tipo de recurso: artículo
Fecha de publicación:2012
País:España
Institución:Universidad de Cantabria (UC)
Repositorio:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:inglés
OAI Identifier:oai:repositorio.unican.es:10902/2962
Acceso en línea:http://hdl.handle.net/10902/2962
Access Level:acceso abierto
Palabra clave:Optimal control of partial differential equations
Nondifferentiable objective
Sparse controls
Finite element discretization
A priori error estimates
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spelling Optimality conditions and error analysis of semilinear elliptic control problems with L1 cost functionalCasas Rentería, Eduardo|||0000-0002-8364-9416Herzog, RolandWachsmuth, GerdOptimal control of partial differential equationsNondifferentiable objectiveSparse controlsFinite element discretizationA priori error estimatesSemilinear elliptic optimal control problems involving the L1 norm of the control in the objective are considered. Necessary and sufficient second-order optimality conditions are derived. A priori finite element error estimates for piecewise constant discretizations for the control and piecewise linear discretizations of the state are shown. Error estimates for the variational discretization of the problem in the sense of [M. Hinze, Comput. Optim. Appl., 30 (2005), pp. 45--61] are also obtained. Numerical experiments confirm the convergence rates.This author was partially supported by the Spanish Ministerio de Economía y Competitividad under the project MTM2011-22711Society for Industrial and Applied MathematicsUniversidad de Cantabria20122012-01-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articlehttp://hdl.handle.net/10902/2962Siam Journal on Control and Optimization, 2012, 22(3), 795-820reponame: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:10902/29622026-06-02T12:39:31Z
dc.title.none.fl_str_mv Optimality conditions and error analysis of semilinear elliptic control problems with L1 cost functional
title Optimality conditions and error analysis of semilinear elliptic control problems with L1 cost functional
spellingShingle Optimality conditions and error analysis of semilinear elliptic control problems with L1 cost functional
Casas Rentería, Eduardo|||0000-0002-8364-9416
Optimal control of partial differential equations
Nondifferentiable objective
Sparse controls
Finite element discretization
A priori error estimates
title_short Optimality conditions and error analysis of semilinear elliptic control problems with L1 cost functional
title_full Optimality conditions and error analysis of semilinear elliptic control problems with L1 cost functional
title_fullStr Optimality conditions and error analysis of semilinear elliptic control problems with L1 cost functional
title_full_unstemmed Optimality conditions and error analysis of semilinear elliptic control problems with L1 cost functional
title_sort Optimality conditions and error analysis of semilinear elliptic control problems with L1 cost functional
dc.creator.none.fl_str_mv Casas Rentería, Eduardo|||0000-0002-8364-9416
Herzog, Roland
Wachsmuth, Gerd
author Casas Rentería, Eduardo|||0000-0002-8364-9416
author_facet Casas Rentería, Eduardo|||0000-0002-8364-9416
Herzog, Roland
Wachsmuth, Gerd
author_role author
author2 Herzog, Roland
Wachsmuth, Gerd
author2_role author
author
dc.contributor.none.fl_str_mv Universidad de Cantabria
dc.subject.none.fl_str_mv Optimal control of partial differential equations
Nondifferentiable objective
Sparse controls
Finite element discretization
A priori error estimates
topic Optimal control of partial differential equations
Nondifferentiable objective
Sparse controls
Finite element discretization
A priori error estimates
description Semilinear elliptic optimal control problems involving the L1 norm of the control in the objective are considered. Necessary and sufficient second-order optimality conditions are derived. A priori finite element error estimates for piecewise constant discretizations for the control and piecewise linear discretizations of the state are shown. Error estimates for the variational discretization of the problem in the sense of [M. Hinze, Comput. Optim. Appl., 30 (2005), pp. 45--61] are also obtained. Numerical experiments confirm the convergence rates.
publishDate 2012
dc.date.none.fl_str_mv 2012
2012-01-01
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/10902/2962
url http://hdl.handle.net/10902/2962
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 Society for Industrial and Applied Mathematics
publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
dc.source.none.fl_str_mv Siam Journal on Control and Optimization, 2012, 22(3), 795-820
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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