A modified subgradient extragradient algorithm-type for solving quasimonotone variational inequality problems with applications

Austine Efut Ofem, Akindele Adebayo Mebawondu, Godwin Chidi Ugwunnadi, Hüseyin Işık*, Ojen Kumar Narain

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

In this article, we introduce an inertial-type algorithm that combines the extragradient subgradient method, the projection contraction method, and the viscosity method. The proposed method is used for solving quasimonotone variational inequality problems in infinite dimensional real Hilbert spaces such that it does not depend on the Lipschitz constant of the cost operator. Further, we prove the strong convergence results of the new algorithm. Our strong convergence results are achieved without imposing strict conditions on the control parameters and inertial factor of our algorithm. We utilize our algorithm to solve some problems in applied sciences and engineering such as image restoration and optimal control. Some numerical experiments are carried out to support our theoretical results. Our numerical illustrations show that our new method is more efficient than many existing methods.

Original languageEnglish
Article number73
JournalJournal of Inequalities and Applications
Volume2023
Issue number1
DOIs
Publication statusPublished - 2023
Externally publishedYes

Keywords

  • Quasimonotone operator
  • Relaxed inertial extragradient subgradient method
  • Strong convergence
  • Variational inequality problem

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