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Applications of convex analysis within mathematics

Opened Access Applications of convex analysis within mathematics

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Autor: Aragón Artacho, Francisco Javier
Borwein, Jonathan M.
Martín Márquez, Victoria
Yao, Liangjin
Departamento: Universidad de Sevilla. Departamento de Análisis Matemático
Fecha: 2014-12
Publicado en: Mathematical Programming, 148 (1), 49-88.
Tipo de documento: Artículo
Resumen: 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.
Cita: Aragón 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.
Tamaño: 617.5Kb
Formato: PDF

URI: http://hdl.handle.net/11441/47195

DOI: 10.1007/s10107-013-0707-3

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