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Semistrictly and neatly quasiconvex programming using lower global subdifferentials

Author

Listed:
  • A. Kabgani

    (University of Antwerp)

  • F. Lara

    (University of Tarapacá)

Abstract

The main goal of this paper is to investigate the properties and connections of neatly and semistrictly quasiconvex functions, especially when they appear in constrained and unconstrained optimization problems. The lower global subdifferential, recently introduced in the literature, plays an essential role in this study. We present several optimality conditions for constrained and unconstrained nonsmooth neatly/semistrictly quasiconvex optimization problems in terms of lower global subdifferentials. To this end, for a constrained optimization problem, we present some characterizations for the normal and tangent cones and the cone of feasible directions of the feasible set. Some relationships between the Greenberg–Pierskalla, tangentially and lower global subdifferentials of neatly and semistrictly quasiconvex functions are also given. The mentioned relationships show that the outcomes of this paper generalize some results existing in the literature.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:86:y:2023:i:4:d:10.1007_s10898-023-01278-9
    DOI: 10.1007/s10898-023-01278-9
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    References listed on IDEAS

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    1. Sorin-Mihai Grad & Felipe Lara, 2022. "An extension of the proximal point algorithm beyond convexity," Journal of Global Optimization, Springer, vol. 82(2), pages 313-329, February.
    2. Nader Kanzi & Majid Soleimani-damaneh, 2020. "Characterization of the weakly efficient solutions in nonsmooth quasiconvex multiobjective optimization," Journal of Global Optimization, Springer, vol. 77(3), pages 627-641, July.
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    7. J. Dutta & S. Chandra, 2002. "Convexifactors, Generalized Convexity, and Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 113(1), pages 41-64, April.
    8. 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.
    9. Felipe Lara, 2020. "Optimality Conditions for Nonconvex Nonsmooth Optimization via Global Derivatives," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 134-150, April.
    10. J.P. Penot, 2003. "Characterization of Solution Sets of Quasiconvex Programs," Journal of Optimization Theory and Applications, Springer, vol. 117(3), pages 627-636, June.
    11. 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.
    12. Satoshi Suzuki, 2021. "Karush–Kuhn–Tucker type optimality condition for quasiconvex programming in terms of Greenberg–Pierskalla subdifferential," Journal of Global Optimization, Springer, vol. 79(1), pages 191-202, January.
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