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

作者：Kuroiwa Daishi; Popovici Nicolae^*; Rocca Matteo

来源：Set-Valued and Variational Analysis, 2015, 23(2): 295-304.

DOI：10.1007/s11228-014-0307-2

• Set-valued affine function
• Cone-convexity
• Cone-quasiconvexity
• Radstrom's cancellation law

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.

• 出版日期2015-6