Scalar representation and conjugation of set-valued functions

To a function with values in the power set of a pre-ordered, separated\nlocally convex space a family of scalarizations is given which completely\ncharacterizes the original function. A concept of a Legendre-Fenchel conjugate\nfor set-valued functions is introduced and identified with the conjugates of\nthe scalarizations. Using this conjugate, weak and strong duality results are\nproven.\n