Computing solutions of the multiclass network equilibrium problem with affine cost functions

@article{Meunier2014ComputingSO,
  title={Computing solutions of the multiclass network equilibrium problem with affine cost functions},
  author={Fr{\'e}d{\'e}ric Meunier and Thomas Pradeau},
  journal={Annals of Operations Research},
  year={2014},
  volume={274},
  pages={447-469}
}
We consider a non-atomic congestion game on a graph, with several classes of players. Each player wants to go from his origin vertex to his destination vertex at the minimum cost and all players of a given class share the same characteristics: cost functions on each arc, and origin–destination pair. Under some mild conditions, it is known that a Nash equilibrium exists, but the computation of such an equilibrium in the multiclass case is an open problem for general functions. We consider the… 

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