A Characterization of Cone-Convexity for Set-Valued Functions by Cone-Quasiconvexity

A Characterization of Cone-Convexity for Set-Valued Functions by Cone-Quasiconvexity

A classical result by Crouzeix ( 1977 ) states that a real-valued function is convex if and only if any function obtained from it by adding a linear functional is quasiconvex. The principal aim of this paper is to present a similar characterization for certain cone-convex set-valued functions by mea...

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Veröffentlicht in:Set-valued and variational analysis 2015-06, Vol.23 (2), p.295-304
Hauptverfasser: Kuroiwa, Daishi, Popovici, Nicolae, Rocca, Matteo
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Mathematics
Mathematics and Statistics
Optimization
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Zusammenfassung:A classical result by Crouzeix ( 1977 ) states that a real-valued function is convex if and only if any function obtained from it by adding a linear functional is quasiconvex. The principal aim of this paper is to present a similar characterization for certain cone-convex set-valued functions by means of cone-quasiconvex and affine set-valued functions.
ISSN:1877-0533
1877-0541
DOI:10.1007/s11228-014-0307-2