On Penalty and Gap Function Methods for Bilevel Equilibrium Problems. (3rd November 2011)

• Record Type: Journal Article
• Authors: Van Dinh, Bui; Muu, Le Dung
• Other Names: Fang Ya Ping Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2011(2011)
• Publication Date: 2011-11-03
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2011/646452
• Languages: English
• ISSNs: 1110-757X

Abstract

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.