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**1 - 3**of**3**### BILEVEL OPTIMIZATION AS A REGULARIZATION APPROACH TO PSEUDOMONOTONE EQUILIBRIUM PROBLEMS

"... Abstract We investigate some properties of an inexact proximal point method for pseudomonotone equilibrium problems in a real Hilbert space. Unlike monotone case, in pseudomonotone case, the regularized subproblems may not be strongly monotone, even not pseudomonotone. However, every proximal traje ..."

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Abstract We investigate some properties of an inexact proximal point method for pseudomonotone equilibrium problems in a real Hilbert space. Unlike monotone case, in pseudomonotone case, the regularized subproblems may not be strongly monotone, even not pseudomonotone. However, every proximal trajectory weakly converges to the same limit, We use these properties to extend a viscosity-proximal point algorithm developed in

### A NEW SOLUTION METHOD FOR PSEUDOMONOTONE EQUILIBRIUM PROBLEMS

"... Abstract We propose a new method for solving an equilibrium problem where the bifunction is pseudomonotone with respect to its solution set. This method can be considered as an extension of the one introduced by Solodov and Svaiter in [28] from variational inequality to equilibrium. An application ..."

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Abstract We propose a new method for solving an equilibrium problem where the bifunction is pseudomonotone with respect to its solution set. This method can be considered as an extension of the one introduced by Solodov and Svaiter in [28] from variational inequality to equilibrium. An application to Nash-Cournot equilibrium models of electricity markets is discussed and its computational results are reported. Bài báo đề xuất một phương pháp mới giải bài toán cân bằng với song hàm cân bằng là giả đơn điệu theo tập nghiệm của nó. Phương pháp này là một sự mở rộng của phương pháp Solodov và Svaiter (xem Index terms Pseudomonotone equilibria, Ky Fan inequality, auxiliary subproblem principle, projection method, Armijo linesearch, Nash-Cournot equilibrium model.

### and applications to quasi-hemivariational inequalities

"... The Tikhonov regularization for equilibrium problems and applications to quasi-hemivariational inequalities ..."

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The Tikhonov regularization for equilibrium problems and applications to quasi-hemivariational inequalities