Second-order optimality conditions for weak and strong local solutions of parabolic optimal control problems

Second-order sufficient optimality conditions are considered for a simplified class of semilinear parabolic equations with quadratic objective functional including distributed and terminal observation. Main emphasis is laid on problems where the objective functional does not include a Tikhonov regul...

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Detalles Bibliográficos
Autores: Casas Rentería, Eduardo|||0000-0002-8364-9416, Tröltzsch, Fredi
Tipo de recurso: artículo
Fecha de publicación:2016
País:España
Institución:Universidad de Cantabria (UC)
Repositorio:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:inglés
OAI Identifier:oai:repositorio.unican.es:10902/11155
Acceso en línea:http://hdl.handle.net/10902/11155
Access Level:acceso abierto
Palabra clave:Optimal control
Parabolic equations
Semilinear equation
Second order optimality conditions
Weak local minimum
Strong local minimum
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spelling Second-order optimality conditions for weak and strong local solutions of parabolic optimal control problemsCasas Rentería, Eduardo|||0000-0002-8364-9416Tröltzsch, FrediOptimal controlParabolic equationsSemilinear equationSecond order optimality conditionsWeak local minimumStrong local minimumSecond-order sufficient optimality conditions are considered for a simplified class of semilinear parabolic equations with quadratic objective functional including distributed and terminal observation. Main emphasis is laid on problems where the objective functional does not include a Tikhonov regularization term. Here, standard second-order conditions cannot be expected to hold. For this case, new second-order conditions are established that are based on different types of critical cones. Depending on the choice of this cones, the second-order conditions are sufficient for local minima that are weak or strong in the sense of calculus of variations.The first author was partially supported by Spanish Ministerio de Economía y Competitividad under projects MTM2011-22711 and MTM2014-57531-P. The second is supported by DFG in the framework of the Collaborative Research Center SFB 910, project B6Springer Science + Business MediaUniversidad de Cantabria20162016-03-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articlehttp://hdl.handle.net/10902/11155Vietnam Journal of Mathematics, 2016, 44(1), 181-202reponame: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:10902/111552026-06-02T12:39:31Z
dc.title.none.fl_str_mv Second-order optimality conditions for weak and strong local solutions of parabolic optimal control problems
title Second-order optimality conditions for weak and strong local solutions of parabolic optimal control problems
spellingShingle Second-order optimality conditions for weak and strong local solutions of parabolic optimal control problems
Casas Rentería, Eduardo|||0000-0002-8364-9416
Optimal control
Parabolic equations
Semilinear equation
Second order optimality conditions
Weak local minimum
Strong local minimum
title_short Second-order optimality conditions for weak and strong local solutions of parabolic optimal control problems
title_full Second-order optimality conditions for weak and strong local solutions of parabolic optimal control problems
title_fullStr Second-order optimality conditions for weak and strong local solutions of parabolic optimal control problems
title_full_unstemmed Second-order optimality conditions for weak and strong local solutions of parabolic optimal control problems
title_sort Second-order optimality conditions for weak and strong local solutions of parabolic optimal control problems
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
Parabolic equations
Semilinear equation
Second order optimality conditions
Weak local minimum
Strong local minimum
topic Optimal control
Parabolic equations
Semilinear equation
Second order optimality conditions
Weak local minimum
Strong local minimum
description Second-order sufficient optimality conditions are considered for a simplified class of semilinear parabolic equations with quadratic objective functional including distributed and terminal observation. Main emphasis is laid on problems where the objective functional does not include a Tikhonov regularization term. Here, standard second-order conditions cannot be expected to hold. For this case, new second-order conditions are established that are based on different types of critical cones. Depending on the choice of this cones, the second-order conditions are sufficient for local minima that are weak or strong in the sense of calculus of variations.
publishDate 2016
dc.date.none.fl_str_mv 2016
2016-03-01
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/10902/11155
url http://hdl.handle.net/10902/11155
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, 2016, 44(1), 181-202
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_ 1869422681790611456
score 15.300719

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