Journal of Convex Analysis 20 (2013), No. 1, 093--106
Copyright Heldermann Verlag 2013
Weak Convexity of the Distance Function
Maxim V. Balashov
Dept. of Higher Mathematics, Moscow Institute of Physics and Technology, Institutskii pereulok 9, Dolgoprudny -- Moscow 141700, Russia
balashov73@mail.ru
We investigate the sets which have neighborhood where the distance function from a point to the set is weakly convex. It is shown that such sets are proximally smooth. We obtain precise estimates for parameters of weak convexity via the size of the neighborhood and the constant of proximal smoothness of the set in the Hilbert space.
Keywords: Distance function, uniform convexity, uniform smoothness, weak convexity, modulus of weak convexity, proximal smoothness, P-supporting condition.
MSC: 49J52, 58C20, 52A07; 52A41, 52A05
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