First and second order conditions for optimal control problems with an L0 term in the cost functional

In this paper, we investigate optimal control problems subject to a semilinear elliptic partial differential equation. The cost functional contains a term that measures the size of the support of the control, which is the so-called L0-norm. We provide necessary and sufficient optimality conditions o...

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Detalles Bibliográficos
Autores: Casas Rentería, Eduardo|||0000-0002-8364-9416, Wachsmuth, Daniel
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:10902/20289
Acceso en línea:http://hdl.handle.net/10902/20289
Access Level:acceso abierto
Palabra clave:Optimal control
Semilinear partial differential equation
Optimality conditions
Sparse controls
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spelling First and second order conditions for optimal control problems with an L0 term in the cost functionalCasas Rentería, Eduardo|||0000-0002-8364-9416Wachsmuth, DanielOptimal controlSemilinear partial differential equationOptimality conditionsSparse controlsIn this paper, we investigate optimal control problems subject to a semilinear elliptic partial differential equation. The cost functional contains a term that measures the size of the support of the control, which is the so-called L0-norm. We provide necessary and sufficient optimality conditions of second order. The sufficient second-order condition is obtained by analyzing a partially convexified problem. Interestingly, the structure of the problem yields second-order conditions with different bilinear forms for the necessary and for the sufficient conditions.The work of the first author was partially supported by the Spanish Ministerio de Economía y Competitividad under research project MTM2017-83185-P. The work of the second author was partially supported by the German Research Foundation (DFG) under project grant Wa 3626/3-2.Society for Industrial and Applied MathematicsUniversidad de Cantabria20202020-01-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articlehttp://hdl.handle.net/10902/20289SIAM Journal on Control and Optimization, 2020, 58(6), 3486-3507reponame: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:10902/202892026-06-02T12:39:31Z
dc.title.none.fl_str_mv First and second order conditions for optimal control problems with an L0 term in the cost functional
title First and second order conditions for optimal control problems with an L0 term in the cost functional
spellingShingle First and second order conditions for optimal control problems with an L0 term in the cost functional
Casas Rentería, Eduardo|||0000-0002-8364-9416
Optimal control
Semilinear partial differential equation
Optimality conditions
Sparse controls
title_short First and second order conditions for optimal control problems with an L0 term in the cost functional
title_full First and second order conditions for optimal control problems with an L0 term in the cost functional
title_fullStr First and second order conditions for optimal control problems with an L0 term in the cost functional
title_full_unstemmed First and second order conditions for optimal control problems with an L0 term in the cost functional
title_sort First and second order conditions for optimal control problems with an L0 term in the cost functional
dc.creator.none.fl_str_mv Casas Rentería, Eduardo|||0000-0002-8364-9416
Wachsmuth, Daniel
author Casas Rentería, Eduardo|||0000-0002-8364-9416
author_facet Casas Rentería, Eduardo|||0000-0002-8364-9416
Wachsmuth, Daniel
author_role author
author2 Wachsmuth, Daniel
author2_role author
dc.contributor.none.fl_str_mv Universidad de Cantabria
dc.subject.none.fl_str_mv Optimal control
Semilinear partial differential equation
Optimality conditions
Sparse controls
topic Optimal control
Semilinear partial differential equation
Optimality conditions
Sparse controls
description In this paper, we investigate optimal control problems subject to a semilinear elliptic partial differential equation. The cost functional contains a term that measures the size of the support of the control, which is the so-called L0-norm. We provide necessary and sufficient optimality conditions of second order. The sufficient second-order condition is obtained by analyzing a partially convexified problem. Interestingly, the structure of the problem yields second-order conditions with different bilinear forms for the necessary and for the sufficient conditions.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-01-01
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/10902/20289
url http://hdl.handle.net/10902/20289
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, 2020, 58(6), 3486-3507
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
_version_ 1869413054493491200
score 15,300724

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