An inertial projection and contraction method for solving bilevel quasimonotone variational inequality problems

J. A. Abuchu*, G. C. Ugwunnadi, O. K. Narain

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

In this paper, we study an iterative algorithm that is based on inertial projection and contraction methods for solving bilevel quasimonotone variational inequality problems in the framework of real Hilbert spaces. We establish a strong convergence result of the proposed iterative method based on adaptive stepsizes conditions without prior knowledge of Lipschitz constant of the cost operator as well as the strongly monotonicity coefficient under some standard mild assumptions on the algorithm parameters. Finally, we present some special numerical experiments to show efficiency and comparative advantage of our algorithm to other related methods in the literature. The results presented in this article improve and generalize some well-known results in the literature.

Original languageEnglish
Pages (from-to)2915-2942
Number of pages28
JournalJournal of Analysis
Volume31
Issue number4
DOIs
Publication statusPublished - Dec 2023
Externally publishedYes

Keywords

  • Bilevel variational inequality
  • Inertial extrapolation method
  • Projection and Contraction method
  • Quasimonotone operator
  • Strong convergence
  • Strongly monotone

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