On solving variational inequality problems involving quasimonotone operators via modified Tseng's extragradient methods with convergence analysis

Volume 27, Issue 1, pp 42--58 http://dx.doi.org/10.22436/jmcs.027.01.04

Publication Date: February 10, 2022 Submission Date: November 29, 2021 Revision Date: December 17, 2021 Accteptance Date: January 06, 2022

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Authors

N. Wairojjana - Applied Mathematics Program, Faculty of Science and Technology, Valaya Alongkorn Rajabhat University under the Royal Patronage, 1 Moo 20 Phaholyothin Road, Klong Neung, Klong Luang, Pathumthani 13180, Thailand. N. Pakkaranang - Mathematics and Computing Science Program, Faculty of Science and Technology, Phetchabun Rajabhat University, Phetchabun 67000, Thailand. S. Noinakorn - Mathematics and Computing Science Program, Faculty of Science and Technology, Phetchabun Rajabhat University, Phetchabun 67000, Thailand.

Abstract

The main objective of this research is to find the numerical solution of variational inequalities involving quasimonotone operators in infinite-dimensional real Hilbert spaces. The main advantage of these iterative schemes is that they allow the uncomplicated calculation of step size rules that depend on the knowledge of an operator explanation instead of the Lipschitz constant or some other line search method. The proposed iterative schemes follow a monotone and non-monotone step size procedure based on mapping (operator) information as a replacement for its Lipschitz constant or some other line search method. The strong convergences are well proven, analogous to the proposed methods, and impose certain control specification conditions. Finally, to verify the effectiveness of the iterative methods, we present some numerical experiments.

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Keywords

• Variational inequality problem
• Tseng's extragradient method
• strong convergence theorems
• quasimonotone operator
• Lipschitz continuity

MSC

•  47J25
•  47H09
•  47H06
•  47J05

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