A class of strongly convergent subgradient extragradient methods for solving quasimonotone variational inequalities
DEMONSTRATIO MATHEMATICA, cilt.56, sa.1, 2023 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 56 Sayı: 1
- Basım Tarihi: 2023
- Doi Numarası: 10.1515/dema-2022-0202
- Dergi Adı: DEMONSTRATIO MATHEMATICA
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Linguistic Bibliography, zbMATH, Directory of Open Access Journals
- Anahtar Kelimeler: variational inequality problem, subgradient extragradient method, strong convergence results, quasimonotone operator, Lipschitz continuity, FIXED-POINTS, SYSTEMS
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Atatürk Üniversitesi Adresli: Evet
Özet
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.