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On Penalty and Gap Function Methods for Bilevel Equilibrium Problems

Bui Van Dinh(vandinhb***at***gmail.com)
Le Dung Muu(ldmuu***at***math.ac.vn)

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 $\nabla$-monotonicity concept from $\nabla$-monotonicity and prove that under pseudo $\nabla$-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 pseudo monotone equilibrium problems

Keywords: Bilevel Equilibrium Problems, Auxiliary Problem Principle, Pseudo $\nabla$-Monotone, Gap Function; Descent Method.

Category 1: Convex and Nonsmooth Optimization

Citation: UNPUBLISHED: 1)report number: 1; 2)Institution address: 1. Bui Van Dinh, Department of Mathematics, Le Quy Don University, No 100, Hoang Quoc Viet, Hanoi, Vietnam; 2. Le Dung Muu, Institute of Mathematics, Hanoi, Vietnam; 3).Month/Year: 06/2011.

Download: [PDF]

Entry Submitted: 06/17/2011
Entry Accepted: 06/17/2011
Entry Last Modified: 06/17/2011

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