On the Duality Theory of Convex Objects

Jan Brinkhuis and V. Tikhomirov

No EI 2001-15, Econometric Institute Research Papers from Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute

Abstract: 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.

Keywords: convex analysis; duality (search for similar items in EconPapers)
JEL-codes: C69 (search for similar items in EconPapers)
Date: 2001-08-13
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Persistent link: https://EconPapers.repec.org/RePEc:ems:eureir:6848

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