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Journal of Optimization Theory and Applications

, Volume 171, Issue 2, pp 384–401 | Cite as

From Quasidifferentiable to Directed Subdifferentiable Functions: Exact Calculus Rules

  • Robert Baier
  • Elza Farkhi
  • Vera Roshchina
Article

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.

Keywords

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

Mathematics Subject Classification

49J52 90C26 26B25 58C20 

Notes

Acknowledgments

We thank Wolfgang Achtziger for motivating us to study the mean-value theorem. This work was partially supported by The Hermann Minkowski Center for Geometry at Tel Aviv University, Tel Aviv, Israel.

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Copyright information

© Springer Science+Business Media New York 2016

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.School of ScienceRMIT UniversityMelbourneAustralia

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