Bilevel mixed equilibrium problems in Banach spaces : existence and algorithmic aspects
Ouayl Chadli, Hicham Mahdioui, Jen‐Chih Yao · Numerical Algebra Control and Optimization · 2011
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).