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Inexact direct-search methods for bilevel optimization problems

Author

Listed:
  • Youssef Diouane

    (Polytechnique Montréal)

  • Vyacheslav Kungurtsev

    (Czech Technical University)

  • Francesco Rinaldi

    (Università di Padova)

  • Damiano Zeffiro

    (Università di Padova)

Abstract

In this work, we introduce new direct-search schemes for the solution of bilevel optimization (BO) problems. Our methods rely on a fixed accuracy blackbox oracle for the lower-level problem, and deal both with smooth and potentially nonsmooth true objectives. We thus analyze for the first time in the literature direct-search schemes in these settings, giving convergence guarantees to approximate stationary points, as well as complexity bounds in the smooth case. We also propose the first adaptation of mesh adaptive direct-search schemes for BO. Some preliminary numerical results on a standard set of bilevel optimization problems show the effectiveness of our new approaches.

Suggested Citation

  • Youssef Diouane & Vyacheslav Kungurtsev & Francesco Rinaldi & Damiano Zeffiro, 2024. "Inexact direct-search methods for bilevel optimization problems," Computational Optimization and Applications, Springer, vol. 88(2), pages 469-490, June.
    • Handle: RePEc:spr:coopap:v:88:y:2024:i:2:d:10.1007_s10589-024-00567-7
    DOI: 10.1007/s10589-024-00567-7
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    References listed on IDEAS

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    1. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
    2. Kwassi Joseph Dzahini, 2022. "Expected complexity analysis of stochastic direct-search," Computational Optimization and Applications, Springer, vol. 81(1), pages 179-200, January.
    3. Shenglong Zhou & Alain B. Zemkoho & Andrey Tin, 2020. "BOLIB: Bilevel Optimization LIBrary of Test Problems," Springer Optimization and Its Applications, in: Stephan Dempe & Alain Zemkoho (ed.), Bilevel Optimization, chapter 0, pages 563-580, Springer.
    4. Ayalew Mersha & Stephan Dempe, 2011. "Direct search algorithm for bilevel programming problems," Computational Optimization and Applications, Springer, vol. 49(1), pages 1-15, May.
    5. Yurii NESTEROV & Vladimir SPOKOINY, 2017. "Random gradient-free minimization of convex functions," LIDAM Reprints CORE 2851, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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