Softening bilevel problems via two-scale Gibbs measures
Carlier, Guillaume; Mallozzi, Lina (2019-10), Softening bilevel problems via two-scale Gibbs measures. https://basepub.dauphine.fr/handle/123456789/20131
TypeDocument de travail / Working paper
External document linkhttps://hal.archives-ouvertes.fr/hal-02305909
Cahier de recherche CEREMADE, Université Paris-Dauphine
Series titleCahier de recherche CEREMADE, Université Paris-Dauphine
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”
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.
Subjects / Keywordsbilevel optimization; Stackelberg games; Gibbs measures; Γ-convergence
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