Scalar Representation and Conjugation of Set-Valued Functions

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.

arXiv admin note: substantial text overlap with arXiv:1012.4357

References in corpus (1)

• Notes about extended real- and set-valued functions

Cited by in corpus (6)

• Set optimization - a rather short introduction
• Lagrange Duality in Set Optimization
• Directional derivatives and subdifferentials of set-valued convex functions
• A Minty variational principle for set optimization
• Set-optimization meets variational inequalities
• Continuity of Convex Set-valued Maps and a Fundamental Duality Formula for Set-valued Optimization