On Penalty and Gap Function Methods for Bilevel Equilibrium Problems

Abstract

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.