Didier Aussel, Daniel Lasluisa, David Salas
Published 2024-03-28Version 1
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.
Bilevel optimal control: existence results and stationarity conditions
On the Proximity of the Optimal Values of the Multi-Dimensional Knapsack Problem with and without the Cardinality Constraint
The sum of root-leaf distance interdiction problem with cardinality constraint by upgrading edges on trees
![QR code for arXiv:2403.19074 [math.OC]](http://oss.arxitics.com/images/favicon.svg)