Article thumbnail

Applications of convex analysis within mathematics

By Francisco Javier Aragón Artacho, Jonathan M. Borwein, Victoria Martín Márquez and Liangjin Yao

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.The authors were all partially supported by various Australian Research Council grants

Topics: 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, Estadística e Investigación Operativa, Análisis Matemático
Year: 2013
OAI identifier: oai:rua.ua.es:10045/29040

Suggested articles


To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.