A Weak Convergence Self-Adaptive Method for Solving Pseudomonotone Equilibrium Problems in a Real Hilbert Space

In this paper, we presented a modification of the extragradient method to solve pseudomonotone equilibrium problems involving the Lipschitz-type condition in a real Hilbert space. The method uses an inertial effect and a formula for stepsize evaluation, that is updated for each iteration based on so...

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Bibliographic Details
Published in:Mathematics (Basel) 2020-07, Vol.8 (7), p.1165
Main Authors: Yordsorn, Pasakorn, Kumam, Poom, Rehman, Habib ur, Hassan Ibrahim, Abdulkarim
Format: Article
Language:English
Subjects:
Algorithms
Convergence
Equilibrium
equilibrium problem
Food science
Hilbert space
Iterative methods
Lipschitz-type conditions
Mathematical problems
Methods
Nash-Cournot oligopolistic equilibrium model
pseudomonotone bifunction
variational inequality problems
weak convergence
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Summary:In this paper, we presented a modification of the extragradient method to solve pseudomonotone equilibrium problems involving the Lipschitz-type condition in a real Hilbert space. The method uses an inertial effect and a formula for stepsize evaluation, that is updated for each iteration based on some previous iterations. The key advantage of the algorithm is that it is achieved without previous knowledge of the Lipschitz-type constants and also without any line search procedure. A weak convergence theorem for the proposed method is well established by assuming mild cost bifunction conditions. Many numerical experiments are presented to explain the computational performance of the method and to equate them with others.
ISSN:2227-7390
2227-7390
DOI:10.3390/math8071165