Generalized Proximal Distances for Bilevel Equilibrium Problems

G. Bento (1) , J. Cruz Neto (2) , J. Lopes (2) , A. Soares Jr (2) , Antoine Soubeyran (3)

1 UFG - Universidade Federal de Goiás [Goiânia]
2 UFPI - Universidade Federal do Piauí
3 GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille

We consider a bilevel problem involving two monotone equilibrium bifunctions and we show that this problem can be solved by a proximal point method with generalized proximal distances. We propose a framework for the convergence analysis of the sequence generated by the algorithm. This class of problems is very interesting because it covers mathematical programs and optimization problems under equilibrium constraints. As an application, we consider the problem of the stability and change dynamics of a leader-follower relationship in a hierarchical organization.

Domains: Humanities and Social Sciences; Economics and Finance; Humanities and Social Sciences; Mathematics [math]

G. Bento, J. Cruz Neto, J. Lopes, A. Soares Jr, Antoine Soubeyran. Generalized Proximal Distances for Bilevel Equilibrium Problems. SIAM Journal on Optimization, 2016, 26 (1), pp.810 - 830. ⟨10.1137/140975589⟩. ⟨hal-01690192⟩