An additive subfamily of enlargements of a maximally monotone operator

We introduce a subfamily of additive enlargements of a maximally monotone operator. Our definition is inspired by the early work of Simon Fitzpatrick. These enlargements constitute a subfamily of the family of enlargements introduced by Svaiter. When the operator under consideration is the subdiffer...

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Autores: Burachik, Regina|||0000-0003-1332-6213, Martínez Legaz, Juan Enrique|||0000-0002-6845-6202, Rezaie, M., Théra, M.
Tipo de recurso: artículo
Fecha de publicación:2015
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:184720
Acceso en línea:https://ddd.uab.cat/record/184720
https://dx.doi.org/urn:doi:10.1007/s11228-015-0340-9
Access Level:acceso abierto
Palabra clave:Maximally monotone operator
ε-subdifferential mapping
Subdifferential operator
Convex lower semicontinuous function
Fitzpatrick function
Enlargement of an operator
Brøndsted- Rockafellar enlargements
Additive enlargements
Brøndsted- Rockafellar property
Fenchel-Young function
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spelling An additive subfamily of enlargements of a maximally monotone operatorBurachik, Regina|||0000-0003-1332-6213Martínez Legaz, Juan Enrique|||0000-0002-6845-6202Rezaie, M.Théra, M.Maximally monotone operatorε-subdifferential mappingSubdifferential operatorConvex lower semicontinuous functionFitzpatrick functionEnlargement of an operatorBrøndsted- Rockafellar enlargementsAdditive enlargementsBrøndsted- Rockafellar propertyFenchel-Young functionWe introduce a subfamily of additive enlargements of a maximally monotone operator. Our definition is inspired by the early work of Simon Fitzpatrick. These enlargements constitute a subfamily of the family of enlargements introduced by Svaiter. When the operator under consideration is the subdifferential of a convex lower semicontinuous proper function, we prove that some members of the subfamily are smaller than the classical ε-subdifferential enlargement widely used in convex analysis. We also recover the ε-subdifferential within the subfamily. Since they are all additive, the enlargements in our subfamily can be seen as structurally closer to the ε-subdifferential enlargement. 22015-01-0120152015-01-01Articlehttp://purl.org/coar/resource_type/c_6501SMURhttp://purl.org/coar/version/c_71e4c1898caa6e32info:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/184720https://dx.doi.org/urn:doi:10.1007/s11228-015-0340-9reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2011-29064-C03open accesshttp://purl.org/coar/access_right/c_abf2Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:1847202026-06-06T12:50:31Z
dc.title.none.fl_str_mv An additive subfamily of enlargements of a maximally monotone operator
title An additive subfamily of enlargements of a maximally monotone operator
spellingShingle An additive subfamily of enlargements of a maximally monotone operator
Burachik, Regina|||0000-0003-1332-6213
Maximally monotone operator
ε-subdifferential mapping
Subdifferential operator
Convex lower semicontinuous function
Fitzpatrick function
Enlargement of an operator
Brøndsted- Rockafellar enlargements
Additive enlargements
Brøndsted- Rockafellar property
Fenchel-Young function
title_short An additive subfamily of enlargements of a maximally monotone operator
title_full An additive subfamily of enlargements of a maximally monotone operator
title_fullStr An additive subfamily of enlargements of a maximally monotone operator
title_full_unstemmed An additive subfamily of enlargements of a maximally monotone operator
title_sort An additive subfamily of enlargements of a maximally monotone operator
dc.creator.none.fl_str_mv Burachik, Regina|||0000-0003-1332-6213
Martínez Legaz, Juan Enrique|||0000-0002-6845-6202
Rezaie, M.
Théra, M.
author Burachik, Regina|||0000-0003-1332-6213
author_facet Burachik, Regina|||0000-0003-1332-6213
Martínez Legaz, Juan Enrique|||0000-0002-6845-6202
Rezaie, M.
Théra, M.
author_role author
author2 Martínez Legaz, Juan Enrique|||0000-0002-6845-6202
Rezaie, M.
Théra, M.
author2_role author
author
author
dc.subject.none.fl_str_mv Maximally monotone operator
ε-subdifferential mapping
Subdifferential operator
Convex lower semicontinuous function
Fitzpatrick function
Enlargement of an operator
Brøndsted- Rockafellar enlargements
Additive enlargements
Brøndsted- Rockafellar property
Fenchel-Young function
topic Maximally monotone operator
ε-subdifferential mapping
Subdifferential operator
Convex lower semicontinuous function
Fitzpatrick function
Enlargement of an operator
Brøndsted- Rockafellar enlargements
Additive enlargements
Brøndsted- Rockafellar property
Fenchel-Young function
description We introduce a subfamily of additive enlargements of a maximally monotone operator. Our definition is inspired by the early work of Simon Fitzpatrick. These enlargements constitute a subfamily of the family of enlargements introduced by Svaiter. When the operator under consideration is the subdifferential of a convex lower semicontinuous proper function, we prove that some members of the subfamily are smaller than the classical ε-subdifferential enlargement widely used in convex analysis. We also recover the ε-subdifferential within the subfamily. Since they are all additive, the enlargements in our subfamily can be seen as structurally closer to the ε-subdifferential enlargement.
publishDate 2015
dc.date.none.fl_str_mv 2
2015-01-01
2015
2015-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
SMUR
http://purl.org/coar/version/c_71e4c1898caa6e32
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/184720
https://dx.doi.org/urn:doi:10.1007/s11228-015-0340-9
url https://ddd.uab.cat/record/184720
https://dx.doi.org/urn:doi:10.1007/s11228-015-0340-9
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2011-29064-C03
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
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
https://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
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