We consider bilevel pseudomonotone equilibrium problems. We use a penalty function to convert a bilevel problem into one-level ones. We generalize a pseudo--monotonicity concept from -monotonicity and prove that under pseudo--monotonicity property any stationary point of a regularized gap function is a solution of the penalized equilibrium problem. As an application, we discuss a special case that arises from the Tikhonov regularization method for pseudomonotone equilibrium problems.
Bui Van Dinh. Le Dung Muu. "On Penalty and Gap Function Methods for Bilevel Equilibrium Problems." J. Appl. Math. 2011 1 - 14, 2011. https://doi.org/10.1155/2011/646452