Journal of Optimization Theory and Applications

, Volume 160, Issue 2, pp 391–414 | Cite as

Directed Subdifferentiable Functions and the Directed Subdifferential Without Delta-Convex Structure

Article

Abstract

We show that the directed subdifferential introduced for differences of convex (delta-convex, DC) functions by Baier and Farkhi can be constructed from the directional derivative without using any information on the delta-convex structure of the function. The new definition extends to a more general class of functions, which includes Lipschitz functions definable on o-minimal structure and quasidifferentiable functions.

Keywords

Nonconvex subdifferentials Directional derivatives Difference of convex (delta-convex, DC) functions Differences of sets 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Chair of Applied MathematicsUniversity of BayreuthBayreuthGermany
  2. 2.School of Mathematical Sciences, Sackler Faculty of Exact SciencesTel Aviv UniversityTel AvivIsrael
  3. 3.Collaborative Research NetworkUniversity of BallaratBallaratAustralia

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