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

Author

Listed:
  • Robert Baier

    (University of Bayreuth)

  • Elza Farkhi

    (Tel Aviv University)

  • Vera Roshchina

    (University of Ballarat)

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.

Suggested Citation

  • Robert Baier & Elza Farkhi & Vera Roshchina, 2014. "Directed Subdifferentiable Functions and the Directed Subdifferential Without Delta-Convex Structure," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 391-414, February.
    • Handle: RePEc:spr:joptap:v:160:y:2014:i:2:d:10.1007_s10957-013-0401-x
    DOI: 10.1007/s10957-013-0401-x
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    References listed on IDEAS

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    1. Robert Baier & Elza Farkhi & Vera Roshchina, 2010. "On Computing the Mordukhovich Subdifferential Using Directed Sets in Two Dimensions," Springer Optimization and Its Applications, in: Regina S. Burachik & Jen-Chih Yao (ed.), Variational Analysis and Generalized Differentiation in Optimization and Control, pages 59-93, Springer.
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    Cited by:

    1. Robert Baier & Elza Farkhi & Vera Roshchina, 2016. "From Quasidifferentiable to Directed Subdifferentiable Functions: Exact Calculus Rules," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 384-401, November.

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    1. Robert Baier & Elza Farkhi & Vera Roshchina, 2016. "From Quasidifferentiable to Directed Subdifferentiable Functions: Exact Calculus Rules," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 384-401, November.

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