A class of strongly convergent subgradient extragradient methods for solving quasimonotone variational inequalities

• Published in: Demonstratio mathematica Vol. 56; no. 1; pp. 1164 - 1173
• Main Authors: Rehman, Habib ur, Kumam, Poom, Ozdemir, Murat, Yildirim, Isa, Kumam, Wiyada
• Format: Journal Article
• Language: English
• Published: De Gruyter 29.07.2023
• Subjects: 47H05; 47H10; 65K15; 65Y05; 68W10; Lipschitz continuity; quasimonotone operator; strong convergence results; subgradient extragradient method; variational inequality problem
• ISSN: 2391-4661; 2391-4661
• DOI: 10.1515/dema-2022-0202

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.