Characterizations of convex functions by level sets

Zoltán Kánnai

Central European Journal of Operations Research, 2024, vol. 32, issue 4, No 8, 1035-1040

Abstract: Abstract It is shown that a lsc function is convex if and only if the minimal set of any linear perturbation of the function is convex. That fact also yields that the convexity of a function is equivalent to the quasiconvexity of its all linear perturbations.

Keywords: Minimal set; Linear perturbation; Convexity of functions; 26B25; 46N10 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10100-024-00908-1

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