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Regular Subgradients of Marginal Functions with Applications to Calculus and Bilevel Programming

Author

Listed:
  • Le Hai

    (Universidad de Tarapacá)

  • Felipe Lara

    (Universidad de Tarapacá)

  • Boris S. Mordukhovich

    (Wayne State University)

Abstract

The paper addresses the study and applications of a broad class of extended-real-valued functions, known as optimal value or marginal functions, which frequently appear in variational analysis, parametric optimization, and a variety of applications. Functions of this type are intrinsically nonsmooth and require the usage of tools of generalized differentiation. The main results of this paper provide novel evaluations and exact calculations of regular/Fréchet subgradients and their singular counterparts for general classes of marginal functions via their given data. The obtained results are applied to establishing new calculus rules for such subgradients and necessary optimality conditions in bilevel programming.

Suggested Citation

  • Le Hai & Felipe Lara & Boris S. Mordukhovich, 2025. "Regular Subgradients of Marginal Functions with Applications to Calculus and Bilevel Programming," Journal of Optimization Theory and Applications, Springer, vol. 205(2), pages 1-30, May.
    • Handle: RePEc:spr:joptap:v:205:y:2025:i:2:d:10.1007_s10957-025-02635-2
    DOI: 10.1007/s10957-025-02635-2
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    References listed on IDEAS

    as
    1. Duong Thi Viet An & Jen-Chih Yao, 2016. "Further Results on Differential Stability of Convex Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 28-42, July.
    2. 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.
    3. Boris S. Mordukhovich, 2020. "Bilevel Optimization and Variational Analysis," Springer Optimization and Its Applications, in: Stephan Dempe & Alain Zemkoho (ed.), Bilevel Optimization, chapter 0, pages 197-226, Springer.
    4. 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.
    Full references (including those not matched with items on IDEAS)

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