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Cardinality Constraints in Single-Leader-Multi-Follower Games

Author

Listed:
  • Didier Aussel

    (Université de Perpignan Via Domitia)

  • Daniel Lasluisa

    (Universidad de Chile)

  • David Salas

    (Universidad de O’Higgins)

Abstract

This work explores bilevel problems in the context of cardinality constraints. More specifically, Single-Leader-Multi-Follower (SLMF) games involving cardinality constraints are considered in two different configurations: one with the cardinality constraint at the leader’s level and a mixed structure in which the cardinality constraint is split between the leader and the followers. We prove existence results in both cases and provide equivalent reformulations allowing the numerical treatment of these complex problems. The results are illustrated thanks to an application to a facility location problem.

Suggested Citation

  • Didier Aussel & Daniel Lasluisa & David Salas, 2025. "Cardinality Constraints in Single-Leader-Multi-Follower Games," Journal of Optimization Theory and Applications, Springer, vol. 206(1), pages 1-27, July.
    • Handle: RePEc:spr:joptap:v:206:y:2025:i:1:d:10.1007_s10957-025-02685-6
    DOI: 10.1007/s10957-025-02685-6
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    References listed on IDEAS

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    1. Christian Kanzow & Andreas B. Raharja & Alexandra Schwartz, 2021. "Sequential optimality conditions for cardinality-constrained optimization problems with applications," Computational Optimization and Applications, Springer, vol. 80(1), pages 185-211, September.
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    4. N. Krejić & E. H. M. Krulikovski & M. Raydan, 2023. "A Low-Cost Alternating Projection Approach for a Continuous Formulation of Convex and Cardinality Constrained Optimization," SN Operations Research Forum, Springer, vol. 4(4), pages 1-24, December.
    5. Thomas Kleinert & Martin Schmidt, 2023. "Why there is no need to use a big-M in linear bilevel optimization: a computational study of two ready-to-use approaches," Computational Management Science, Springer, vol. 20(1), pages 1-12, December.
    6. Jong-Shi Pang & Masao Fukushima, 2005. "Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games," Computational Management Science, Springer, vol. 2(1), pages 21-56, January.
    7. Max Bucher & Alexandra Schwartz, 2018. "Second-Order Optimality Conditions and Improved Convergence Results for Regularization Methods for Cardinality-Constrained Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 383-410, August.
    8. Vladimir Marianov, 2003. "Location of Multiple-Server Congestible Facilities for Maximizing Expected Demand, when Services are Non-Essential," Annals of Operations Research, Springer, vol. 123(1), pages 125-141, October.
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    10. Matteo Fischetti & Ivana Ljubić & Michele Monaci & Markus Sinnl, 2019. "Interdiction Games and Monotonicity, with Application to Knapsack Problems," INFORMS Journal on Computing, INFORMS, vol. 31(2), pages 390-410, April.
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