Abstract

It is shown that for some classes of functions all epiderivatives and subdifferentials of F.H.Clarke type and P.Michel–J.-P.Penot type and others coincide. Several rules of calculation of subdifferentials for the difference of two convex functions are obtained. Some examples are considered.

Author information

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

Evgeny Sergeevich Polovinkin

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

polovinkin@mail.mipt.ru

Keywords

  • Set-valued map
  • tangent cone
  • convex function
  • semiregular function
  • Lipschitz continuity
  • epiderivatives
  • subdifferentials

Mathematics Subject Classification

49K22, 49K24; 49J22, 49J24

Suggested citation

E. S. Polovinkin. “Calculation of Subdifferentials for the Difference of Two Convex Functions.” Journal of Convex Analysis 24 (2017), No. 1, 287–303.

Copyright Banach Press 2017