A unified framework for three accelerated extragradient methods and further acceleration for variational inequality problems

The main strategy of this paper is intended to speed up the convergence of the inertial Mann iterative method and further speed up it through the normal S-iterative method for a certain class of nonexpansive-type operators that are linked with variational inequality problems. Our new convergence the...

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Bibliographic Details
Published in:Soft computing (Berlin, Germany) Germany), 2023-11, Vol.27 (21), p.15649-15674
Main Author: Sahu, D. R.
Format: Article
Language:English
Subjects:
Acceleration
Algorithms
Artificial Intelligence
Codes
Computational Intelligence
Control
Convergence
Efficiency
Engineering
Hilbert space
Iterative methods
Mathematical Logic and Foundations
Mechatronics
Methods
Optimization
Ordinary differential equations
Robotics
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Summary:The main strategy of this paper is intended to speed up the convergence of the inertial Mann iterative method and further speed up it through the normal S-iterative method for a certain class of nonexpansive-type operators that are linked with variational inequality problems. Our new convergence theory permits us to settle down the difficulty of unification of Korpelevich’s extragradient method, Tseng’s extragardient method, and subgardient extragardient method for solving variational inequality problems through an auxiliary algorithmic operator, which is associated with the seed operator. The paper establishes an interesting the fact that the relaxed inertial normal S-iterative extragradient methods do influence much more on convergence behaviour. Finally, the numerical experiments are carried out to illustrate that the relaxed inertial iterative methods; in particular, the relaxed inertial normal S-iterative extragradient methods may have a number of advantages over other methods in computing solutions to variational inequality problems in many cases.
ISSN:1432-7643
1433-7479
DOI:10.1007/s00500-023-08806-5