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Characterizations of Nonsmooth Robustly Quasiconvex Functions

Author

Listed:
  • Hoa T. Bui

    (Federation University Australia)

  • Pham Duy Khanh

    (HCMC University of Education
    Universidad de Chile)

  • Thi Tu Trinh Tran

    (Oakland University Michigan)

Abstract

Two criteria for the robust quasiconvexity of lower semicontinuous functions are established in terms of Fréchet subdifferentials in Asplund spaces. The first criterion extends to such spaces a result established by Barron et al. (Discrete Contin Dyn Syst Ser B 17:1693–1706, 2012). The second criterion is totally new even if it is applied to lower semicontinuous functions on finite-dimensional spaces.

Suggested Citation

  • Hoa T. Bui & Pham Duy Khanh & Thi Tu Trinh Tran, 2019. "Characterizations of Nonsmooth Robustly Quasiconvex Functions," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 775-786, March.
    • Handle: RePEc:spr:joptap:v:180:y:2019:i:3:d:10.1007_s10957-018-1421-3
    DOI: 10.1007/s10957-018-1421-3
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    References listed on IDEAS

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    1. J.-P. Penot & P. H. Quang, 1997. "Generalized Convexity of Functions and Generalized Monotonicity of Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 92(2), pages 343-356, February.
    2. D. Aussel, 1998. "Subdifferential Properties of Quasiconvex and Pseudoconvex Functions: Unified Approach," Journal of Optimization Theory and Applications, Springer, vol. 97(1), pages 29-45, April.
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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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