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Softening bilevel problems via two-scale Gibbs measures

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soft-Stackelberg-final.pdf (998.2Kb)
Date
2019-10
Publisher city
Paris
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Publishing date
2019
Collection title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Link to item file
https://hal.archives-ouvertes.fr/hal-02305909
Dewey
Analyse
Sujet
bilevel optimization; Stackelberg games; Gibbs measures; Γ-convergence
URI
https://basepub.dauphine.fr/handle/123456789/20131
Collections
  • CEREMADE : Publications
Metadata
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Author
Carlier, Guillaume
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Mallozzi, Lina
42093 Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”
Type
Document de travail / Working paper
Item number of pages
27
Abstract (EN)
We introduce a new, and elementary, approximation method for bilevel optimization problems motivated by Stackelberg leader-follower games. Our technique is based on the notion of two-scale Gibbs measures. The first scale corresponds to the cost function of the follower and the second scale to that of the leader. We explain how to choose the weights corresponding to these two scales under very general assumptions and establish rigorous Γ-convergence results. An advantage of our method is that it is applicable both to optimistic and to pessimistic bilevel problems.

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