Approximation of elliptic control problems in measure spaces with sparse solutions

Optimal control problems in measure spaces governed by elliptic equations are considered for distributed and Neumann boundary control, which are known to promote sparse solutions. Optimality conditions are derived and some of the structural properties of their solutions, in particular sparsity, are...

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Detalhes bibliográficos
Autores: Casas Rentería, Eduardo|||0000-0002-8364-9416, Clason, Christian, Kunisch, Karl
Formato: artículo
Fecha de publicación:2012
País:España
Recursos:Universidad de Cantabria (UC)
Repositorio:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:inglés
OAI Identifier:oai:repositorio.unican.es:10902/2210
Acesso em linha:http://hdl.handle.net/10902/2210
Access Level:acceso abierto
Palavra-chave:Measure controls
Optimal control
Sparsity
Elliptic partial differential equation
Convergence estimates
Boundary control
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spelling Approximation of elliptic control problems in measure spaces with sparse solutionsCasas Rentería, Eduardo|||0000-0002-8364-9416Clason, ChristianKunisch, KarlMeasure controlsOptimal controlSparsityElliptic partial differential equationConvergence estimatesBoundary controlOptimal control problems in measure spaces governed by elliptic equations are considered for distributed and Neumann boundary control, which are known to promote sparse solutions. Optimality conditions are derived and some of the structural properties of their solutions, in particular sparsity, are discussed. A framework for their approximation is proposed which is efficient for numerical computations and for which we prove convergence and provide error estimates.This author was supported by Spanish Ministerio de Ciencia e Innovación under projects MTM2008-04206 and “Ingenio Mathematica (i-MATH)” CSD2006-00032 (Consolider Ingenio 2010).Society 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/10902/2210SIAM Journal on Control and Optimization, 2012, 50(4), 1735–1752reponame: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:10902/22102026-06-02T12:39:31Z
dc.title.none.fl_str_mv Approximation of elliptic control problems in measure spaces with sparse solutions
title Approximation of elliptic control problems in measure spaces with sparse solutions
spellingShingle Approximation of elliptic control problems in measure spaces with sparse solutions
Casas Rentería, Eduardo|||0000-0002-8364-9416
Measure controls
Optimal control
Sparsity
Elliptic partial differential equation
Convergence estimates
Boundary control
title_short Approximation of elliptic control problems in measure spaces with sparse solutions
title_full Approximation of elliptic control problems in measure spaces with sparse solutions
title_fullStr Approximation of elliptic control problems in measure spaces with sparse solutions
title_full_unstemmed Approximation of elliptic control problems in measure spaces with sparse solutions
title_sort Approximation of elliptic control problems in measure spaces with sparse solutions
dc.creator.none.fl_str_mv Casas Rentería, Eduardo|||0000-0002-8364-9416
Clason, Christian
Kunisch, Karl
author Casas Rentería, Eduardo|||0000-0002-8364-9416
author_facet Casas Rentería, Eduardo|||0000-0002-8364-9416
Clason, Christian
Kunisch, Karl
author_role author
author2 Clason, Christian
Kunisch, Karl
author2_role author
author
dc.contributor.none.fl_str_mv Universidad de Cantabria
dc.subject.none.fl_str_mv Measure controls
Optimal control
Sparsity
Elliptic partial differential equation
Convergence estimates
Boundary control
topic Measure controls
Optimal control
Sparsity
Elliptic partial differential equation
Convergence estimates
Boundary control
description Optimal control problems in measure spaces governed by elliptic equations are considered for distributed and Neumann boundary control, which are known to promote sparse solutions. Optimality conditions are derived and some of the structural properties of their solutions, in particular sparsity, are discussed. A framework for their approximation is proposed which is efficient for numerical computations and for which we prove convergence and provide error estimates.
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/10902/2210
url http://hdl.handle.net/10902/2210
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, 50(4), 1735–1752
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 15.300719

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