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Softening bilevel problems via two-scale Gibbs measures

hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorCarlier, Guillaume
hal.structure.identifierDipartimento di Matematica e Applicazioni “Renato Caccioppoli”
dc.contributor.authorMallozzi, Lina
dc.date.accessioned2019-10-14T11:33:27Z
dc.date.available2019-10-14T11:33:27Z
dc.date.issued2019
dc.identifier.issn1877-0541
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/20131
dc.language.isoenen
dc.subjectbilevel optimization
dc.subjectStackelberg games
dc.subjectGibbs measures
dc.subjectΓ-convergence
dc.subject.ddc515en
dc.titleSoftening bilevel problems via two-scale Gibbs measures
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe 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.
dc.publisher.cityParisen
dc.relation.isversionofjnlnameSet-Valued and Variational Analysis
dc.relation.isversionofjnlvol30
dc.relation.isversionofjnldate2019
dc.relation.isversionofjnlpages573–595
dc.relation.isversionofdoi10.1007/s11228-021-00605-0
dc.relation.isversionofjnlpublisherSpringer
dc.subject.ddclabelAnalyseen
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2023-02-04T13:56:27Z
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