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On global subdifferentials with applications in nonsmooth optimization

Author

Listed:
  • Felipe Lara

    (Universidad de Tarapacá)

  • Alireza Kabgani

    (Urmia University of Technology
    Institute for Research in Fundamental Sciences (IPM))

Abstract

The notions of global subdifferentials associated with the global directional derivatives are introduced in the following paper. Most common used properties, a set of calculus rules along with a mean value theorem are presented as well. In addition, a diversity of comparisons with well-known subdifferentials such as Fréchet, Dini, Clarke, Michel–Penot, and Mordukhovich subdifferential and convexificator notion are provided. Furthermore, the lower global subdifferential is in fact proved to be an abstract subdifferential. Therefore, the lower global subdifferential satisfies standard properties for subdifferential operators. Finally, two applications in nonconvex nonsmooth optimization are given: necessary and sufficient optimality conditions for a point to be local minima with and without constraints, and a revisited characterization for nonsmooth quasiconvex functions.

Suggested Citation

  • Felipe Lara & Alireza Kabgani, 2021. "On global subdifferentials with applications in nonsmooth optimization," Journal of Global Optimization, Springer, vol. 81(4), pages 881-900, December.
    • Handle: RePEc:spr:jglopt:v:81:y:2021:i:4:d:10.1007_s10898-020-00981-1
    DOI: 10.1007/s10898-020-00981-1
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    References listed on IDEAS

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    Cited by:

    1. A. Kabgani & F. Lara, 2022. "Strong subdifferentials: theory and applications in nonconvex optimization," Journal of Global Optimization, Springer, vol. 84(2), pages 349-368, October.
    2. A. Kabgani & F. Lara, 2023. "Semistrictly and neatly quasiconvex programming using lower global subdifferentials," Journal of Global Optimization, Springer, vol. 86(4), pages 845-865, August.

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