We consider bilevel pseudomonotone equilibrium problems. We use a penalty function to convert a bilevel problem into one-level ones. We generalize a pseudo $\nabla$-monotonicity concept from $\nabla$-monotonicity and prove that under pseudo $\nabla$-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 pseudo monotone equilibrium problems
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UNPUBLISHED: 1)report number: 1; 2)Institution address: 1. Bui Van Dinh, Department of Mathematics, Le Quy Don University, No 100, Hoang Quoc Viet, Hanoi, Vietnam; 2. Le Dung Muu, Institute of Mathematics, Hanoi, Vietnam; 3).Month/Year: 06/2011.
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