On the Duality Theory of Convex Objects
2001-08-13
Research Paper
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We 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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Automatically Extracted Terms
- vectorspace v
- subspace
- vectorspace
- theorem
- function
- element
- subset
- result
- statement
- space
- vector
- vector space v
- sublinear functions
- conjugate cone
- affine subspace
- affine
- hahn-banach
- vector space
- sublinear
- object
