A class of strongly convergent subgradient extragradient methods for solving quasimonotone variational inequalities
- Resource Type
- article
- Authors
- Rehman Habib ur; Kumam Poom; Ozdemir Murat; Yildirim Isa; Kumam Wiyada
- Source
- Demonstratio Mathematica, Vol 56, Iss 1, Pp 1164-1173 (2023)
- Subject
- variational inequality problem
subgradient extragradient method
strong convergence results
quasimonotone operator
lipschitz continuity
65y05
65k15
68w10
47h05
47h10
Mathematics
QA1-939
- Language
- English
- ISSN
- 2391-4661
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.