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On Quasiconvex Functions Which are Convexifiable or Not

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Abstract

A quasiconvex function f being given, does there exist an increasing and continuous function k which makes \(k\circ f\) convex? How to build such a k? Some words on least convex (concave) functions. The ratio of two positive numbers is neither locally convexifiable nor locally concavifiable. Finally, some considerations on the approximation of a preorder from a finite number of observations and on the revealed preference problem are discussed.

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Acknowledgements

The author is very grateful to the referees for their careful readings. Their corrections, comments and remarks have been precious; the paper has been improved greatly thanks to the help of the referees.

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  1. LIMOS, Université Clermont Auvergne, 1 Rue de la Chebarde, 63178, Aubière, France

    Jean-Pierre Crouzeix

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  1. Jean-Pierre Crouzeix
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Correspondence to Jean-Pierre Crouzeix.

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Communicated by Boris S. Mordukhovich.

Dedicated to Franco Gianessi.

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Crouzeix, JP. On Quasiconvex Functions Which are Convexifiable or Not. J Optim Theory Appl 193, 66–80 (2022). https://doi.org/10.1007/s10957-021-01965-1

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  • DOI: https://doi.org/10.1007/s10957-021-01965-1

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