Scalar Representation and Conjugation of Set-Valued Functions

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. Using this conjugate, weak and strong duality results are proven.