Applications of convex analysis within mathematics
Copyright policy )Applications of convex analysis within mathematics
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.
38 pages, minor revision incorporating referees' comments
- University of Newcastle Australia Australia
- Carma United States
- University of Seville Spain
- University of Alicante Spain
- King Abdulaziz University Saudi Arabia
convex functions, maximally monotone operator, Infimal convolution, Hahn-Banach extension theorem, Maximally monotone operator, Sandwich theorem, Yosida approximation, Moreau’s decomposition, Chebyshev set, Adjoint, 90C25, Moreau envelope, 47B65, Fenchel duality, Monotone operator, Primary 47N10, Estadística e Investigación Operativa, linear relation, subdifferential operator, normal cone operator, Renorming, resolvent, Moreau's decomposition, Moreau’s max formula, Mathematics - Optimization and Control, 47A06, Fitzpatrick function, Análisis Matemático, Sub-differential operator, sum theorem, Primary 47N10, 90C25, Secondary 47H05, 47A06, 47B65, Secondary 47H05, Functional Analysis (math.FA), Mathematics - Functional Analysis, autoconjugate representer, Moreau's max formula, asplund averaging, Fenchel conjugate, monotone operator, Normal cone operator, Minty surjectivity theorem, renorming, Linear relation, Banach limit, resolvent, Renorming, Asplund averaging, FOS: Mathematics, infimal convolution, Sum theorem, Resolvent, convex function, adjoint, Convex functions, Subdifferential operator, Autoconjugate representer, Moreau-Rockafellar duality, Optimization and Control (math.OC)
convex functions, maximally monotone operator, Infimal convolution, Hahn-Banach extension theorem, Maximally monotone operator, Sandwich theorem, Yosida approximation, Moreau’s decomposition, Chebyshev set, Adjoint, 90C25, Moreau envelope, 47B65, Fenchel duality, Monotone operator, Primary 47N10, Estadística e Investigación Operativa, linear relation, subdifferential operator, normal cone operator, Renorming, resolvent, Moreau's decomposition, Moreau’s max formula, Mathematics - Optimization and Control, 47A06, Fitzpatrick function, Análisis Matemático, Sub-differential operator, sum theorem, Primary 47N10, 90C25, Secondary 47H05, 47A06, 47B65, Secondary 47H05, Functional Analysis (math.FA), Mathematics - Functional Analysis, autoconjugate representer, Moreau's max formula, asplund averaging, Fenchel conjugate, monotone operator, Normal cone operator, Minty surjectivity theorem, renorming, Linear relation, Banach limit, resolvent, Renorming, Asplund averaging, FOS: Mathematics, infimal convolution, Sum theorem, Resolvent, convex function, adjoint, Convex functions, Subdifferential operator, Autoconjugate representer, Moreau-Rockafellar duality, Optimization and Control (math.OC)
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