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

Creative Commons License

Rehman H. U., Kumam P., Ozdemir M., Yildirim İ., Kumam W.

DEMONSTRATIO MATHEMATICA, cilt.56, sa.1, 2023 (SCI-Expanded) identifier identifier

  • 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
  • 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.