Characterizations of convex functions by level sets

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.

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Year of publication:	2024
Authors:	Kánnai, Zoltán
Publisher:	Springer
Subject:	Mathematics \| Econometrics

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Type of publication:	Article
Language:	English
Notes:	Kánnai, Zoltán (2024) Characterizations of convex functions by level sets. Central European Journal of Operations Research . DOI https://doi.org/10.1007/s10100-024-00908-1
Other identifiers:	10.1007/s10100-024-00908-1 [DOI]
Source:	BASE

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