Conjugate Duality of Set--Valued Functions
Carola Schrage

TL;DR
This paper introduces a conjugate duality framework for set-valued functions in pre-ordered locally convex spaces, using scalarizations and extending classical conjugation concepts to the set-valued context.
Contribution
It develops a Legendre-Fenchel conjugate for set-valued functions and links it with scalarizations and duality theories, advancing the mathematical foundation of set-valued analysis.
Findings
Scalarizations fully characterize set-valued functions.
A new Legendre-Fenchel conjugate for set-valued functions is defined.
Duality results connect conjugation with $(*,s)$--dualities.
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. The concept of conjugation is connected to the notion of --dualities and duality results are provided.
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Taxonomy
TopicsOptimization and Variational Analysis · Advanced Optimization Algorithms Research · Functional Equations Stability Results
