Generalized Proximal Distances for Bilevel Equilibrium Problems

G. Bento, J. Cruz Neto, J. Lopes, A. Soares Jr and Antoine Soubeyran
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G. Bento: UFG - Universidade Federal de Goiás [Goiânia]
J. Cruz Neto: UFPI - Universidade Federal do Piauí
J. Lopes: UFPI - Universidade Federal do Piauí
A. Soares Jr: UFPI - Universidade Federal do Piauí

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Abstract: 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.

Date: 2016-01
Note: View the original document on HAL open archive server: https://amu.hal.science/hal-01690192
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Citations: View citations in EconPapers (5)

Published in SIAM Journal on Optimization, 2016, 26 (1), pp.810 - 830. ⟨10.1137/140975589⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01690192

DOI: 10.1137/140975589

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