Set-Valued Evenly Convex Functions: Characterizations and C-Conjugacy

In this work we deal with set-valued functions with values in the power set of a separated locally convex space where a nontrivial pointed convex cone induces a partial order relation. A set-valued function is evenly convex if its epigraph is an evenly convex set, i.e., it is the intersection of an...

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Bibliographic Details
Published in:Set-valued and variational analysis Vol. 30; no. 3; pp. 827 - 846
Main Author: Fajardo, M. D.
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.09.2022
Springer Nature B.V
Subjects:
Analysis
Conjugation
Half spaces
Mathematics
Mathematics and Statistics
Optimization
Original Research
Partially ordered spaces
Fenchel-Moreau theorem
52A41
Evenly convex sets
90C25
Set-valued functions
49N15
Convex conjugation
ISSN:1877-0533, 1877-0541
Online Access:Get full text
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Summary:In this work we deal with set-valued functions with values in the power set of a separated locally convex space where a nontrivial pointed convex cone induces a partial order relation. A set-valued function is evenly convex if its epigraph is an evenly convex set, i.e., it is the intersection of an arbitrary family of open half-spaces. In this paper we characterize evenly convex set-valued functions as the pointwise supremum of its set-valued e-affine minorants. Moreover, a suitable conjugation pattern will be developed for these functions, as well as the counterpart of the biconjugation Fenchel-Moreau theorem.
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ISSN:1877-0533
1877-0541
DOI:10.1007/s11228-021-00621-0