1. A class of strongly convergent subgradient extragradient methods for solving quasimonotone variational inequalities
- Author
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Rehman Habib ur, Kumam Poom, Ozdemir Murat, Yildirim Isa, and Kumam Wiyada
- Subjects
variational inequality problem ,subgradient extragradient method ,strong convergence results ,quasimonotone operator ,lipschitz continuity ,65y05 ,65k15 ,68w10 ,47h05 ,47h10 ,Mathematics ,QA1-939 - Abstract
The primary goal of this research is to investigate the approximate numerical solution of variational inequalities using quasimonotone operators in infinite-dimensional real Hilbert spaces. In this study, the sequence obtained by the proposed iterative technique for solving quasimonotone variational inequalities converges strongly toward a solution due to the viscosity-type iterative scheme. Furthermore, a new technique is proposed that uses an inertial mechanism to obtain strong convergence iteratively without the requirement for a hybrid version. The fundamental benefit of the suggested iterative strategy is that it substitutes a monotone and non-monotone step size rule based on mapping (operator) information for its Lipschitz constant or another line search method. This article also provides a numerical example to demonstrate how each method works.
- Published
- 2023
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