A dynamical approach for the quantitative stability of parametric bilevel equilibrium problems and applications

Optimization ◽  
2021 ◽  
pp. 1-20
Author(s):  
Mohamed Ait Mansour ◽  
Zakaria Mazgouri ◽  
Hassan Riahi
Keyword(s):  
Equilibrium Problems ◽  
Quantitative Stability ◽  
Dynamical Approach ◽  
Bilevel Equilibrium Problems

scholarly journals Generalized Proximal Distances for Bilevel Equilibrium Problems

2016 ◽  
Vol 26 (1) ◽  
pp. 810-830 ◽  
Author(s):  
G. C. Bento ◽  
J. X. Cruz Neto ◽  
J. O. Lopes ◽  
P. A. Soares Jr ◽  
A. Soubeyran
Keyword(s):  
Equilibrium Problems ◽  
Bilevel Equilibrium Problems

scholarly journals An inertial extragradient method for solving bilevel equilibrium problems

2020 ◽  
Vol 36 (1) ◽  
pp. 91-107
Author(s):  
JIRAPRAPA MUNKONG ◽  
BUI VAN DINH ◽  
KASAMSUK UNGCHITTRAKOOL
Keyword(s):  
Hilbert Space ◽  
Numerical Experiment ◽  
Equilibrium Problems ◽  
Real Hilbert Space ◽  
Extragradient Method ◽  
Iteration Process ◽  
Iterative Sequence ◽  
Inertial Term ◽  
Speed Up ◽  
Bilevel Equilibrium Problems

In this paper, we propose an algorithm with two inertial term extrapolation steps for solving bilevel equilibrium problem in a real Hilbert space. The inertial term extrapolation step is introduced to speed up the rate of convergence of the iteration process. Under some sufficient assumptions on the bifunctions involving pseudomonotone and Lipschitz-type conditions, we obtain the strong convergence of the iterative sequence generated by the proposed algorithm. A numerical experiment is performed to illustrate the numerical behavior of the algorithm and also comparison with some other related algorithms in the literature.

scholarly journals On Penalty and Gap Function Methods for Bilevel Equilibrium Problems

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Bui Van Dinh ◽  
Le Dung Muu
Keyword(s):  
Tikhonov Regularization ◽  
Penalty Function ◽  
Stationary Point ◽  
Regularization Method ◽  
Equilibrium Problems ◽  
Monotonicity Property ◽  
Gap Function ◽  
Tikhonov Regularization Method ◽  
Bilevel Equilibrium Problems ◽  
Special Case

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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