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.

convex analysis, duality
Mathematical Methods and Programming: Other (jel C69)
Tinbergen Institute Discussion Paper Series , Econometric Institute Research Papers
Erasmus School of Economics

Brinkhuis, J, & Tikhomirov, V. (2001). On the Duality Theory of Convex Objects (No. EI 2001-15). Econometric Institute Research Papers. Retrieved from http://hdl.handle.net/1765/6848