Geodesic
Concavifying the Quasiconcave
Journal of convex analysis, Tome 24 (2017) no. 4, pp. 1239-1262
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We revisit a classic question of Fenchel from 1953: Which quasiconcave functions can be concavified by post-composition with a monotonic transformation? This question has a long history in economic utility theory. While many authors have given partial answers under various assumptions, we offer a complete characterization for quasiconcave functions without a priori assumptions on regularity. The answer hinges on the local regularity class of the function.
Classification : 52A41, 26A51, 26B25, 46N10
Mots-clés : Concavifiability, convexifiability, quasi-concavity, quasi-convexity 
@article{JCA_2017_24_4_JCA_2017_24_4_a8,
     author = {C. Connell and E. B. Rasmusen},
     title = {Concavifying the {Quasiconcave}},
     journal = {Journal of convex analysis},
     pages = {1239--1262},
     year = {2017},
     volume = {24},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JCA_2017_24_4_JCA_2017_24_4_a8/}
}
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C. Connell; E. B. Rasmusen. Concavifying the Quasiconcave. Journal of convex analysis, Tome 24 (2017) no. 4, pp. 1239-1262. http://geodesic.mathdoc.fr/item/JCA_2017_24_4_JCA_2017_24_4_a8/