Conjugate Duality of Set--Valued Functions

Details Conjugate Duality of Set--Valued Functions Conjugate Duality of Set--Valued Functions

2010-12-20

arxiv.org/abs/1012.4357v3

Mathematics

Optimization and Control

arXiv admin note: substantial text overlap with arXiv:1011.5860

Scientific paper

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 $(*,s)$--dualities and duality results are provided.

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