Inertial Extra-Gradient Method for Solving a Family of Strongly Pseudomonotone Equilibrium Problems in Real Hilbert Spaces with Application in Variational Inequality Problem

In this paper, we propose a new method, which is set up by incorporating an inertial step with the extragradient method for solving a strongly pseudomonotone equilibrium problems. This method had to comply with a strongly pseudomonotone property and a certain Lipschitz-type condition of a bifunction...

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Bibliographic Details
Published in:Symmetry (Basel) 2020-04, Vol.12 (4), p.503
Main Authors: Rehman, Habib ur, Kumam, Poom, Argyros, Ioannis K., Deebani, Wejdan, Kumam, Wiyada
Format: Article
Language:English
Subjects:
Algorithms
Convergence
Equilibrium
equilibrium problem
Hilbert space
Hilbert spaces
Iterative methods
lipschitz-like conditions
Mathematical problems
Methods
strong convergence theorem
strongly pseudomonotone equilibrium problems
two-step extragradient method
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Summary:In this paper, we propose a new method, which is set up by incorporating an inertial step with the extragradient method for solving a strongly pseudomonotone equilibrium problems. This method had to comply with a strongly pseudomonotone property and a certain Lipschitz-type condition of a bifunction. A strong convergence result is provided under some mild conditions, and an iterative sequence is accomplished without previous knowledge of the Lipschitz-type constants of a cost bifunction. A sufficient explanation is that the method operates with a slow-moving stepsize sequence that converges to zero and non-summable. For numerical explanations, we analyze a well-known equilibrium model to support our well-established convergence result, and we can see that the proposed method seems to have a significant consistent improvement over the performance of the existing methods.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym12040503