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arXiv · 1011.5860

Scalar Representation and Conjugation of Set-Valued Functions

Carola Schrage
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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.

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Carola Schrage. 2010-11-26. Scalar Representation and Conjugation of Set-Valued Functions. https://doi.org/10.1080/02331934.2012.741126

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