Inertial self-adaptive Bregman projection method for finite family of variational inequality problems in reflexive Banach spaces

O. K. Oyewole, L. O. Jolaoso*, K. O. Aremu, M. O. Olayiwola

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

This paper considers an iterative approximation of a common solution of a finite family of variational inequailties in a real reflexive Banach space. By employing the Bregman distance and projection methods, we propose an iterative algorithm which uses a newly constructed adaptive step size to avoid a dependence on the Lipschitz constants of the families of the cost operators. The algorithm is carefully constructed so that the need to find a farthest element in any of its iterate is avoided. A strong convergence theorem was proved using the proposed method. We report some numerical experiments to illustrate the performance of the algorithm and also compare with existing methods in the literature.

Original languageEnglish
Article number273
JournalComputational and Applied Mathematics
Volume41
Issue number6
DOIs
Publication statusPublished - Sep 2022

Keywords

  • Extragradient method
  • Projection
  • Pseudomonotone
  • Reflexive banach space
  • Variational inequalities

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