Journal of Applied Mathematics

On Penalty and Gap Function Methods for Bilevel Equilibrium Problems

Bui Van Dinh and Le Dung Muu

Full-text: Open access

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.

Article information

Source
J. Appl. Math., Volume 2011 (2011), Article ID 646452, 14 pages.

Dates
First available in Project Euclid: 15 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1331818662

Digital Object Identifier
doi:10.1155/2011/646452

Mathematical Reviews number (MathSciNet)
MR2846448

Zentralblatt MATH identifier
1242.49068

Citation

Van Dinh, Bui; Muu, Le Dung. On Penalty and Gap Function Methods for Bilevel Equilibrium Problems. J. Appl. Math. 2011 (2011), Article ID 646452, 14 pages. doi:10.1155/2011/646452. https://projecteuclid.org/euclid.jam/1331818662


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