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On the Duality Theory of Convex Objects

Author

Listed:
  • Brinkhuis, J.
  • Tikhomirov, V.

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.

Suggested Citation

  • Brinkhuis, J. & Tikhomirov, V., 2001. "On the Duality Theory of Convex Objects," Econometric Institute Research Papers EI 2001-15, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:6848
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    File URL: https://repub.eur.nl/pub/6848/2001-0751.pdf
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    More about this item

    Keywords

    convex analysis; duality;

    JEL classification:

    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other

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