Cardinality Constraints in Single-Leader-Multi-Follower Games

Didier Aussel (), Daniel Lasluisa () and David Salas ()
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Didier Aussel: Université de Perpignan Via Domitia
Daniel Lasluisa: Universidad de Chile
David Salas: Universidad de O’Higgins

Journal of Optimization Theory and Applications, 2025, vol. 206, issue 1, No 16, 27 pages

Abstract: 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.

Keywords: Cardinality constraints; Bilevel optimization; Single-Leader-Multi-Follower games; Location problem; 49J52; 49J53; 91A10; 90-10 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02685-6

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