Three novel inertial explicit Tseng's extragradient methods for solving pseudomonotone variational inequalities

Rehman H. U., Kumam P., ÖZDEMİR M., Argyros I. K., Kumam W.

OPTIMIZATION, cilt.71, sa.16, ss.4697-4730, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 71 Sayı: 16
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1080/02331934.2021.1963248
  • Dergi Adı: OPTIMIZATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, ABI/INFORM, Aerospace Database, Applied Science & Technology Source, Computer & Applied Sciences, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.4697-4730
  • Anahtar Kelimeler: Variational inequalities, Tseng's extragradient method, inertial methods, pseudomonotone mapping, strong convergence theorem, FIXED-POINTS
  • Atatürk Üniversitesi Adresli: Evet

Özet

In this paper, we construct three new extragradient-type iterative methods for solving variational inequalities in real Hilbert spaces. The proposed iterative methods are functionally equivalent to the extragradient method, which is used to solve variational inequalities in an infinite-dimensional real Hilbert space. The main advantage of these iterative methods is that they use a simple step size rule based on operator information instead of the Lipschitz constant or any line search method. Three strong convergence theorems are well proved, corresponding to the proposed methods by allowing certain control parameter conditions. Finally, we present some numerical experiments to verify the efficacy and superiority of the proposed iterative methods.