Generalized Proximal Distances for Bilevel Equilibrium Problems | Zendy

G. C. Bento | Zendy; J. X. Cruz Neto | Zendy; J. O. Lopes | Zendy; P. A. Soares | Zendy; Antoine Soubeyran | Zendy

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Generalized Proximal Distances for Bilevel Equilibrium Problems

Author(s) -

G. C. Bento,

J. X. Cruz Neto,

J. O. Lopes,

P. A. Soares,

Antoine Soubeyran

Publication year - 2016

Publication title -

siam journal on optimization

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.066

H-Index - 136

eISSN - 1095-7189

pISSN - 1052-6234

DOI - 10.1137/140975589

Subject(s) - bilevel optimization , mathematical optimization , convergence (economics) , monotone polygon , class (philosophy) , sequence (biology) , stability (learning theory) , point (geometry) , equilibrium point , computer science , optimization problem , mathematics , artificial intelligence , mathematical analysis , geometry , machine learning , biology , economics , genetics , differential equation , economic growth

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.

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