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.
A Characterization of Cone-Convexity for Set-Valued Functions by Cone-Quasiconvexity
ROCCA, MATTEO
2015-01-01
Abstract
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.
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