On Quasiconvex Functions Which are Convexifiable or Not

Jean-Pierre Crouzeix ()
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Jean-Pierre Crouzeix: LIMOS, Université Clermont Auvergne

Journal of Optimization Theory and Applications, 2022, vol. 193, issue 1, No 5, 66-80

Abstract: Abstract A quasiconvex function f being given, does there exist an increasing and continuous function k which makes $$k\circ f$$ k ∘ 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.

Keywords: Convexifiability; Least concavity; Preorder; Utility functions; Afriat’s and sandwich approximations; Revealed preferences; 91B42; 26B25 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10957-021-01965-1

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