Applications of convex analysis within mathematics

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Title: Applications of convex analysis within mathematics
Authors: Aragón Artacho, Francisco Javier | Borwein, Jonathan M. | Martín Márquez, Victoria | Yao, Liangjin
Research Group/s: Laboratorio de Optimización (LOPT)
Center, Department or Service: Universidad de Alicante. Departamento de Estadística e Investigación Operativa
Keywords: Adjoint | Asplund averaging | Autoconjugate representer | Banach limit | Chebyshev set | Convex functions | Fenchel duality | Fenchel conjugate | Fitzpatrick function | Hahn-Banach extension theorem | Infimal convolution | Linear relation | Minty surjectivity theorem | Maximally monotone operator | Monotone operator | Moreau's decomposition | Moreau envelope | Moreau's max formula | Moreau-Rockafellar duality | Normal cone operator | Renorming | Resolvent | Sandwich theorem | Sub-differential operator | Sum theorem | Yosida approximation
Knowledge Area: Estadística e Investigación Operativa | Análisis Matemático
Issue Date: 8-Feb-2013
Abstract: In 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 auto-conjugate representers for maximally monotone operators. Finally, we consider various other applications in mathematical analysis.
Sponsor: The authors were all partially supported by various Australian Research Council grants.
URI: http://hdl.handle.net/10045/29040
Language: eng
Type: info:eu-repo/semantics/preprint
Peer Review: no
Appears in Collections:INV - LOPT - Artículos de Revistas

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