Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Maxim V. Balashov

Dept. of Higher Mathematics, Moscow Institute of Physics and Technology, Institutskii pereulok 9, Dolgoprudny -- Moscow 141700, Russia

balashov73@mail.ru

Keywords

  • Distance function
  • uniform convexity
  • uniform smoothness
  • weak convexity
  • modulus of weak convexity
  • proximal smoothness
  • P-supporting condition

Mathematics Subject Classification

49J52, 58C20, 52A07; 52A41, 52A05

Suggested citation

M. V. Balashov. “Weak Convexity of the Distance Function.” Journal of Convex Analysis 20 (2013), No. 1, 93–106.

Copyright Heldermann Verlag 2013