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

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

DEMONSTRATIO MATHEMATICA, vol.56, no.1, 2023 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 56 Issue: 1
  • Publication Date: 2023
  • Doi Number: 10.1515/dema-2022-0202
  • Journal Name: DEMONSTRATIO MATHEMATICA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Linguistic Bibliography, zbMATH, Directory of Open Access Journals
  • Keywords: variational inequality problem, subgradient extragradient method, strong convergence results, quasimonotone operator, Lipschitz continuity, FIXED-POINTS, SYSTEMS
  • Open Archive Collection: AVESIS Open Access Collection
  • Ataturk University Affiliated: Yes

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.