On the Duality Theory of Convex Objects
AbstractWe consider the classical duality operators for convex objects such as the polar of a convex set containing the origin, the dual norm, the Fenchel-transform of a convex function and the conjugate of a convex cone. We give a new, sharper, unified treatment of the theory of these operators, deriving generalized theorems of Hahn-Banach, Fenchel-Moreau and Dubovitsky-Milyutin for the conjugate of convex cones in not necessarily finite dimensional vector spaces and hence for all the other duality operators of convex objects.
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Bibliographic InfoPaper provided by Erasmus University Rotterdam, Econometric Institute in its series Econometric Institute Report with number EI 2001-15.
Date of creation: 13 Aug 2001
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duality; convex analysis;
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