On Penalty and Gap Function Methods for Bilevel Equilibrium Problems

Abstract EN

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.