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On the Duality Theory of Convex Objects

Author

Listed:
  • J. Brinkhuis

    (Erasmus University Rotterdam)

  • V. Tikhomirov

    (Moscow State University)

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.

Suggested Citation

  • J. Brinkhuis & V. Tikhomirov, 2001. "On the Duality Theory of Convex Objects," Tinbergen Institute Discussion Papers 01-075/1, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20010075
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