On Bilevel Monotone Inclusion and Variational Inequality Problems

Austine Efut Ofem*, Jacob Ashiwere Abuchu, Hossam A. Nabwey*, Godwin Chidi Ugwunnadi, Ojen Kumar Narain

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this article, the problem of solving a strongly monotone variational inequality problem over the solution set of a monotone inclusion problem in the setting of real Hilbert spaces is considered. To solve this problem, two methods, which are improvements and modifications of the Tseng splitting method, and projection and contraction methods, are presented. These methods are equipped with inertial terms to improve their speed of convergence. The strong convergence results of the suggested methods are proved under some standard assumptions on the control parameters. Also, strong convergence results are achieved without prior knowledge of the operator norm. Finally, the main results of this research are applied to solve bilevel variational inequality problems, convex minimization problems, and image recovery problems. Some numerical experiments to show the efficiency of our methods are conducted.

Original languageEnglish
Article number4643
JournalMathematics
Volume11
Issue number22
DOIs
Publication statusPublished - Nov 2023
Externally publishedYes

Keywords

  • Tseng method
  • inertial term
  • monotone inclusion problem
  • projection and contraction method
  • strong convergence
  • variational inequality problem

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