Abstract
The Fenchel problem of level sets was formulated by Roberts and Varberg in their book titled “Convex functions” (1973, p. 271) is as follows: “What “nice” conditions on a nested family of convex sets will ensure that it is the family of level sets of a convex function?” The aim of the paper is to draw attention to this structural question of convex analysis and to survey some results in different directions.
This research was supported in part by the Hungarian National Research Fund, Grant No. OTKA-TO43241 and CNR.
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Rapcsák, T. (2005). Survey on the Fenchel Problem of Level Sets. In: Giannessi, F., Maugeri, A. (eds) Variational Analysis and Applications. Nonconvex Optimization and Its Applications, vol 79. Springer, Boston, MA. https://doi.org/10.1007/0-387-24276-7_54
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DOI: https://doi.org/10.1007/0-387-24276-7_54
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