Single Bregman projection method for solving variational inequalities in reflexive Banach spaces

Lateef O. Jolaoso, Yekini Shehu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)

Abstract

In this paper, we introduce a single projection method with the Bregman distance technique for solving pseudomonotone variational inequalities in a real reflexive Banach space. The algorithm is designed such that its step size is determined by a self-adaptive process and there is only one computation of projection per iteration during implementation. This improves the convergence of the method and also avoids the need for choosing a suitable estimate of the Lipschitz constant of the cost function which is very difficult in practice. We prove some weak and strong convergence results under suitable conditions on the cost operator. We also provide some numerical experiments to illustrate the performance and efficiency of the proposed method.

Original languageEnglish
Pages (from-to)4807-4828
Number of pages22
JournalApplicable Analysis
Volume101
Issue number14
DOIs
Publication statusPublished - 2022

Keywords

  • Banach spaces
  • Variational inequalities
  • pseudomonotone mapping
  • self-adaptive step size
  • single projection method

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