From Quasidifferentiable to Directed Subdifferentiable Functions: Exact Calculus Rules

Robert Baier, Elza Farkhi, Vera Roshchina

Research output: Contribution to journalArticlepeer-review

Abstract

We derive exact calculus rules for the directed subdifferential defined for the class of directed subdifferentiable functions. We also state optimality conditions, a chain rule and a mean-value theorem. Thus, we extend the theory of the directed subdifferential from quasidifferentiable to directed subdifferentiable functions.

Original languageEnglish
Pages (from-to)384-401
Number of pages18
JournalJournal of Optimization Theory and Applications
Volume171
Issue number2
DOIs
StatePublished - 1 Nov 2016

Keywords

  • Difference of convex (DC) functions
  • Directional derivatives
  • Mean-value theorem and chain rule for nonsmooth functions
  • Nonconvex subdifferentials

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