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Cardinality Constraints in Single-Leader-Multi-Follower games

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arxiv 2403.19074 v1 pith:W2RSYEGC submitted 2024-03-28 math.OC

Didier Aussel , Daniel Lasluisa , David Salas This is my paper · ORCID
classification math.OC
keywords cardinalityconstraintsconstraintgamesleaderproblemproblemsresults
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This work explores bilevel problems in the context of cardinality constraints. More specifically Single-Leader-Multi-Follower games (SLMFG) 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 leader and followers problem. We prove existence results in both cases and provided equivalent reformulations allowing the numerical treatment of these complex problems. The obtained results are illustrated thanks to an application to a facility location problem.

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  1. A Cardinality-Constrained Approach to Combinatorial Bilevel Congestion Pricing

    math.OC 2024-12 conditional novelty 7.0 of 10

    A penalty decomposition with cardinality constraints and block coordinate descent solves combinatorial bilevel congestion pricing at 3,000-link scale with convergence to an approximate KKT point.

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