Geodesic
A Clarke–Ledyaev Type Inequality for Certain Non–Convex Sets
Serdica Mathematical Journal, Tome 26 (2000) no. 4, pp. 277-286.

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We consider the question whether the assumption of convexity of the set involved in Clarke-Ledyaev inequality can be relaxed. In the case when the point is outside the convex hull of the set we show that Clarke-Ledyaev type inequality holds if and only if there is certain geometrical relation between the point and the set.
Keywords: Nonsmooth Analysis, Mean Value Theorem, Subdifferential 
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     author = {Ivanov, M. and Zlateva, N.},
     title = {A {Clarke{\textendash}Ledyaev} {Type} {Inequality} for {Certain} {Non{\textendash}Convex} {Sets}},
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Ivanov, M.; Zlateva, N. A Clarke–Ledyaev Type Inequality for Certain Non–Convex Sets. Serdica Mathematical Journal, Tome 26 (2000) no. 4, pp. 277-286. http://geodesic.mathdoc.fr/item/SMJ2_2000_26_4_a0/