Abstract
For a convex continuous function f:X→R, the smoothness of the set {x∈X|f(x)≤r} is characterized by a differentiability property of f. Questions of this kind arise from optimization problems and gauge functionals, e.g. in the theory of Orlicz spaces.
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Literatur
HOLMES, R. B.: A Course on Optimization and Best Approximation; Lecture Notes in Math. 257, Springer 1972.
KÖTHE, G.: Topologische lineare Räume I; Berlin-Heidelberg-New York, Springer 1966.
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Kosmol, P. Flache Konvexität und Schwache Differenzierbarkeit. Manuscripta Math 8, 267–270 (1973). https://doi.org/10.1007/BF01297691
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DOI: https://doi.org/10.1007/BF01297691