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From Quasidifferentiable to Directed Subdifferentiable Functions: Exact Calculus Rules

Author

Listed:
  • Robert Baier

    (University of Bayreuth)

  • Elza Farkhi

    (Tel Aviv University)

  • Vera Roshchina

    (RMIT University)

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.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:171:y:2016:i:2:d:10.1007_s10957-016-0926-x
    DOI: 10.1007/s10957-016-0926-x
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    References listed on IDEAS

    as
    1. Y. Gao, 2004. "Representation of the Clarke Generalized Jacobian via the Quasidifferential," Journal of Optimization Theory and Applications, Springer, vol. 123(3), pages 519-532, December.
    2. 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.
    3. 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.
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    Cited by:

    1. Alireza Kabgani, 2021. "Characterization of Nonsmooth Quasiconvex Functions and their Greenberg–Pierskalla’s Subdifferentials Using Semi-Quasidifferentiability notion," Journal of Optimization Theory and Applications, Springer, vol. 189(2), pages 666-678, May.

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