Applications of convex analysis within mathematics |
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Authors: | Francisco J Aragón Artacho Jonathan M Borwein Victoria Martín-Márquez Liangjin Yao |
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Institution: | 1. Centre for Computer Assisted Research Mathematics and Its Applications (CARMA), University of Newcastle, Callaghan, NSW, 2308, Australia 2. King Abdul-Aziz University, Jeddah, Saudi Arabia 3. Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, PO Box 1160, 41080?, Sevilla, Spain
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Abstract: | In this paper, we study convex analysis and its theoretical applications. We first apply important tools of convex analysis to Optimization and to Analysis. We then 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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