Scalar Representation and Conjugation of Set-Valued Functions
Optimization and Control
2014-05-29 v4
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.
Cite
@article{arxiv.1011.5860,
title = {Scalar Representation and Conjugation of Set-Valued Functions},
author = {Carola Schrage},
journal= {arXiv preprint arXiv:1011.5860},
year = {2014}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1012.4357