On the Duality Theory of Convex Objects

J. Brinkhuis () and V. Tikhomirov
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J. Brinkhuis: Erasmus University Rotterdam
V. Tikhomirov: Moscow State University

No 01-075/1, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: We consider the classical duality operators for convex objects suchas the polar of a convex set containing the origin, the dual norm,the Fenchel-transform of a convex function and the conjugate of aconvex cone. We give a new, sharper, unified treatment of the theoryof these operators, deriving generalized theorems of Hahn-Banach,Fenchel-Moreau and Dubovitsky-Milyutin for the conjugate of convexcones in not necessarily finite dimensional vector spaces and hencefor all the other duality operators of convex objects.

Date: 2001-08-13
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Persistent link: https://EconPapers.repec.org/RePEc:tin:wpaper:20010075

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