Applications of convex analysis within mathematics
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http://hdl.handle.net/10045/29040
| Títol: | Applications of convex analysis within mathematics |
|---|---|
| Autors: | Aragón Artacho, Francisco Javier | Borwein, Jonathan M. | Martín Márquez, Victoria | Yao, Liangjin |
| Grups d'investigació o GITE: | Laboratorio de Optimización (LOPT) |
| Centre, Departament o Servei: | Universidad de Alicante. Departamento de Estadística e Investigación Operativa |
| Paraules clau: | 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 |
| Àrees de coneixement: | Estadística e Investigación Operativa | Análisis Matemático |
| Data de publicació: | 8-de febrer-2013 |
| Resum: | 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. |
| Patrocinadors: | The authors were all partially supported by various Australian Research Council grants. |
| URI: | http://hdl.handle.net/10045/29040 |
| Idioma: | eng |
| Tipus: | info:eu-repo/semantics/preprint |
| Revisió científica: | no |
| Apareix a la col·lecció: | INV - LOPT - Artículos de Revistas |
Arxius per aquest ítem:
| Arxiu | Descripció | Tamany | Format | |
|---|---|---|---|---|
 2013_Aragon_etal.pdf | 617,58 kB | Adobe PDF | Obrir Vista prèvia | |
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