Conjugate Duality of Set--Valued Functions
arXiv:1012.4357
Abstract
To a function with values in the power set of a pre--ordered, separated locally convex space a family of scalarizations is given which completely characterizes the original function. A concept of a Legendre--Fenchel conjugate for set-valued functions is introduced and identified with the conjugates of the scalarizations. The concept of conjugation is connected to the notion of --dualities and duality results are provided.
This paper has been withdrawn by the author. Withdrawn. This paper was an early version of arXiv:1011.5860