Bilevel mixed equilibrium problems in Banach spaces : existence and algorithmic aspects

Ouayl Chadli; Hicham Mahdioui; Jen-Chih Yao

doi:10.3934/naco.2011.1.549

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2011, Volume 1, Issue 3: 549-561. Doi: 10.3934/naco.2011.1.549

This issue Previous Article Asymptotic strong duality Next Article

Bilevel mixed equilibrium problems in Banach spaces : existence and algorithmic aspects

1.
Department of Economics, Ibn Zohr University, B.P. 8658 Poste Dakhla, Agadir
2.
Department of Mathematics, Ibn Zohr University, Agadir
3.
Kaohsiung Medical University, Kaohsiung Medical University, Kaohsiung 80708

Received: May 2011

Revised: August 2011

Published: August 2011

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Abstract

In this paper, we study the existence and algorithmic aspect of a class of bilevel mixed equilibrium problems (BMEP) in a Banach space setting. We introduce a suitable regularization of the bilevel mixed equilibrium problems by means of an auxiliary equilibrium problem. We show that it is possible to define from the auxiliary equilibrium problems a sequence strongly convergent to a solution of the bilevel mixed equilibrium problem. The results obtained are interesting in the sense that they improve some new results on bilevel mixed equilibrium problems and give answer to some open questions in literature related to the convergence of algorithms for (BMEP).

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Mathematics Subject Classification: Primary: 47J20, 49J40, 49J45; Secondary: 49M20, 47H05, 90C30.

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