On Penalty and Gap Function Methods for Bilevel Equilibrium Problems

Bui Van Dinh and Le Dung Muu

Journal of Applied Mathematics, 2011, vol. 2011, issue 1

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.

Date: 2011
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https://doi.org/10.1155/2011/646452

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2011:y:2011:i:1:n:646452

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