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Applications of convex analysis within mathematics

dc.creatorAragón Artacho, Francisco Javieres
dc.creatorBorwein, Jonathan M.es
dc.creatorMartín Márquez, Victoriaes
dc.creatorYao, Liangjines
dc.date.accessioned2016-10-07T11:05:11Z
dc.date.available2016-10-07T11:05:11Z
dc.date.issued2014-12
dc.identifier.citationAragón Artacho, F.J., Borwein, J.M., Martín Márquez, V. y Yao, L. (2014). Applications of convex analysis within mathematics. Mathematical Programming, 148 (1), 49-88.
dc.identifier.issn0025-5610es
dc.identifier.issn1436-4646es
dc.identifier.urihttp://hdl.handle.net/11441/47195
dc.description.abstractIn this paper, we study convex analysis and its theoretical applications. We apply important tools of convex analysis to Optimization and to Analysis. Then we show various deep applications of convex analysis and especially infimal convolution in Monotone Operator Theory. Among other things, we recapture the Minty surjectivity theorem in Hilbert space, and present a new proof of the sum theorem in reflexive spaces. More technically, we also discuss autoconjugate representers for maximally monotone operators. Finally, we consider various other applications in mathematical analysis.es
dc.description.sponsorshipAustralian Research Counciles
dc.formatapplication/pdfes
dc.language.isoenges
dc.publisherSpringeres
dc.relation.ispartofMathematical Programming, 148 (1), 49-88.
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internacional*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subjectAdjointes
dc.subjectAsplund averaginges
dc.subjectAutoconjugate representeres
dc.subjectBanach limites
dc.subjectChebyshev setes
dc.subjectConvex functionses
dc.subjectFenchel dualityes
dc.subjectFenchel conjugatees
dc.subjectFitzpatrick functiones
dc.subjectHahn-Banach extension theoremes
dc.subjectInfimal convolutiones
dc.subjectLinear relationes
dc.subjectMinty surjectivity theoremes
dc.subjectMaximally monotone operatores
dc.subjectMonotone operatores
dc.subjectMoreau’s decompositiones
dc.subjectMoreau envelopees
dc.subjectMoreau’s max formulaes
dc.subjectMoreau-Rockafellar dualityes
dc.subjectNormal cone operatores
dc.subjectRenorming, resolventes
dc.subjectSandwich theoremes
dc.subjectSubdifferential operatores
dc.subjectSum theoremes
dc.subjectYosida approximationes
dc.titleApplications of convex analysis within mathematicses
dc.typeinfo:eu-repo/semantics/articlees
dcterms.identifierhttps://ror.org/03yxnpp24
dc.type.versioninfo:eu-repo/semantics/submittedVersiones
dc.rights.accessRightsinfo:eu-repo/semantics/openAccesses
dc.contributor.affiliationUniversidad de Sevilla. Departamento de Análisis Matemáticoes
dc.relation.publisherversionhttp://download.springer.com/static/pdf/312/art%253A10.1007%252Fs10107-013-0707-3.pdf?originUrl=http%3A%2F%2Flink.springer.com%2Farticle%2F10.1007%2Fs10107-013-0707-3&token2=exp=1475839336~acl=%2Fstatic%2Fpdf%2F312%2Fart%25253A10.1007%25252Fs10107-013-0707-3.pdf%3ForiginUrl%3Dhttp%253A%252F%252Flink.springer.com%252Farticle%252F10.1007%252Fs10107-013-0707-3*~hmac=bf170fadafb51a4e14bf5e842ed761f58d8d4566a4ed8d48025bfdb8debeb15ees
dc.identifier.doi10.1007/s10107-013-0707-3es
dc.contributor.groupUniversidad de Sevilla. FQM127: Análisis Funcional no Lineales
idus.format.extent37 p.es
dc.journaltitleMathematical Programminges
dc.publication.volumen148es
dc.publication.issue1es
dc.publication.initialPage49es
dc.publication.endPage88es
dc.identifier.idushttps://idus.us.es/xmlui/handle/11441/47195
dc.contributor.funderAustralian Research Council

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