Two-step inertial Tseng's extragradient method for solving quasimonotone variational inequalities

We focus on quasimonotone variational inequality problems with non-Lipschitz operator and combine some operator theory techniques to establish a weak convergent fixed point iterative method to approximate the solution of the presented problems. The convergence analysis assumes very mild conditions a...

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Bibliographic Details
Published in:Quaestiones mathematicae 2024-07, Vol.47 (7), p.1505-1543
Main Authors: Mewomo, O.T., Nwokoye, R.N., Okeke, C.C.
Format: Article
Language:English
Subjects:
Algorithms
Armijo-like step size technique
Cost analysis
Hilbert spaces
inertial extrapolation
Iterative methods
Quasimonotone variational inequalities
Tseng extragradient method
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Summary:We focus on quasimonotone variational inequality problems with non-Lipschitz operator and combine some operator theory techniques to establish a weak convergent fixed point iterative method to approximate the solution of the presented problems. The convergence analysis assumes very mild conditions and strictly weaker assumption on the cost operator associated with the problems and thus generalizes and extend recent related results in the literature. Finally, several numerical examples illustrate the potential and advantages of the proposed algorithm over some existing methods are presented.
ISSN:1607-3606
1727-933X
DOI:10.2989/16073606.2024.2327562