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

Robert Baier, Elza Farkhi, Vera Roshchina

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)391-414
Number of pages24
JournalJournal of Optimization Theory and Applications
Volume160
Issue number2
DOIs
StatePublished - Feb 2014

Keywords

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

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