Weak convergence of explicit extragradient algorithms for solving equilibirum problems
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Author list: ur Rehman H., Kumam P., Cho Y.J., Yordsorn P.
Publisher: SpringerOpen
Publication year: 2019
Journal: Journal of Inequalities and Applications (1025-5834)
Volume number: 2019
Issue number: 1
ISSN: 1025-5834
eISSN: 1029-242X
Languages: English-Great Britain (EN-GB)
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Abstract
This paper aims to propose two new algorithms that are developed by implementing inertial and subgradient techniques to solve the problem of pseudomonotone equilibrium problems. The weak convergence of these algorithms is well established based on standard assumptions of a cost bi-function. The advantage of these algorithms was that they did not need a line search procedure or any information on Lipschitz-type bifunction constants for step-size evaluation. A practical explanation for this is that they use a sequence of step-sizes that are updated at each iteration based on some previous iterations. For numerical examples, we discuss two well-known equilibrium models that assist our well-established convergence results, and we see that the suggested algorithm has a competitive advantage over time of execution and the number of iterations. ฉ 2019, The Author(s).
Keywords
Lipschitz-type conditions, Nash–Cournot equilibrium model of electricity markets
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