Scalar Representation and Conjugation of Set-Valued Functions

Details Scalar Representation and Conjugation of Set-Valued Functions Scalar Representation and Conjugation of Set-Valued Functions

2010-11-26

arxiv.org/abs/1011.5860v3

Mathematics

Optimization and Control

arXiv admin note: substantial text overlap with arXiv:1012.4357

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

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