A SELF-ADAPTIVE POPOV'S EXTRAGRADIENT METHOD FOR SOLVING EQUILIBRIUM PROBLEMS WITH APPLICATIONS

Wairojjana N., Rehman H. U., Pakkaranang N., Hussain A., Khanpanuk T.

Journal of Mathematical Analysis, vol.11, no.4, pp.45-60, 2020 (ESCI, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 4
  • Publication Date: 2020
  • Journal Name: Journal of Mathematical Analysis
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.45-60
  • Keywords: Equilibrium problem, Hilbert space, Lipschitz-type continuous, Pseudomonotone, Weak convergence
  • Uşak University Affiliated: No

Abstract

In this paper, we suggest a new method to solve the pseudomonotone equilibrium problem. This method can be seen as an extension and improvement of the Popov's extragradient method. We replace the fixed stepsize with a self-adapting stepsize formula that is revised on each iteration depends on previous iterations. A weak convergence theorem of the method is well established based on typical bifunctional cost assumptions. We also provide the application of our results to solve two kinds of variational inequality problems. Various numerical examples are provided to support our well-established convergence results, and we can see that the new approach provides a significant improvement in the number of iterations and the execution time.