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On Penalty and Gap Function Methods for Bilevel Equilibrium Problems

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  • Bui Van Dinh
  • Le Dung Muu

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.

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  • Bui Van Dinh & Le Dung Muu, 2011. "On Penalty and Gap Function Methods for Bilevel Equilibrium Problems," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-14, November.
    • Handle: RePEc:hin:jnljam:646452
    DOI: 10.1155/2011/646452
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    Cited by:

    1. Seifu Endris Yimer & Poom Kumam & Anteneh Getachew Gebrie & Rabian Wangkeeree, 2019. "Inertial Method for Bilevel Variational Inequality Problems with Fixed Point and Minimizer Point Constraints," Mathematics, MDPI, vol. 7(9), pages 1-21, September.
    2. G. Bento & J. Cruz Neto & J. Lopes & A. Soares Jr & Antoine Soubeyran, 2016. "Generalized Proximal Distances for Bilevel Equilibrium Problems," Post-Print hal-01690192, HAL.

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