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Softening bilevel problems via two-scale Gibbs measures

Carlier, Guillaume; Mallozzi, Lina (2019), Softening bilevel problems via two-scale Gibbs measures, Set-Valued and Variational Analysis, 30, p. 573–595. 10.1007/s11228-021-00605-0

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Type
Article accepté pour publication ou publié
Date
2019
Journal name
Set-Valued and Variational Analysis
Volume
30
Publisher
Springer
Published in
Paris
Pages
573–595
Publication identifier
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Author(s)
Carlier, Guillaume
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Mallozzi, Lina
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 / Keywords
bilevel optimization; Stackelberg games; Gibbs measures; Γ-convergence