Applications of convex analysis within mathematics
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 reca...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2014 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/47195 |
| Acceso en línea: | http://hdl.handle.net/11441/47195 https://doi.org/10.1007/s10107-013-0707-3 |
| Access Level: | acceso abierto |
| Palabra clave: | 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 Subdifferential operator Sum theorem Yosida approximation |
| Sumario: | 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 autoconjugate representers for maximally monotone operators. Finally, we consider various other applications in mathematical analysis. |
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