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

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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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Authors and Affiliations

  1. Department of Mathematics and Computer Sciences, Shimane University, Matsue, 690-8504, Japan

    Daishi Kuroiwa

  2. Faculty of Mathematics and Computer Science, Babeş-Bolyai University of Cluj-Napoca, 400084, Cluj-Napoca, Romania

    Nicolae Popovici

  3. Department of Economics, University of Insubria, 21100, Varese, Italy

    Matteo Rocca

Authors
  1. Daishi Kuroiwa
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  2. Nicolae Popovici
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  3. Matteo Rocca
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Correspondence to Nicolae Popovici.

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Kuroiwa, D., Popovici, N. & Rocca, M. A Characterization of Cone-Convexity for Set-Valued Functions by Cone-Quasiconvexity. Set-Valued Var. Anal 23, 295–304 (2015). https://doi.org/10.1007/s11228-014-0307-2

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  • DOI: https://doi.org/10.1007/s11228-014-0307-2

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