Fast and Simple Bregman Projection Methods for Solving Variational Inequalities and Related Problems in Banach Spaces

Aviv Gibali*, Lateef Olakunle Jolaoso, Oluwatosin Temitope Mewomo, Adeolu Taiwo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)

Abstract

In this paper, we study the problem of finding a common solution to variational inequality and fixed point problems for a countable family of Bregman weak relatively nonexpansive mappings in real reflexive Banach spaces. Two inertial-type algorithms with adaptive step size rules for solving the problem are presented and their strong convergence theorems are established. The usage of the Bregman distances and the Armijo line search technique (which avoids the need to know a priori the Lipschitz constant of the involved operators), enable great flexibility of the proposed scheme, and besides their theoretical extensions, it might also have a practical potential.

Original languageEnglish
Article number179
JournalResults in Mathematics
Volume75
Issue number4
DOIs
Publication statusPublished - 1 Dec 2020
Externally publishedYes

Keywords

  • Banach spaces
  • Bregman weak relatively nonexpansive mappings
  • Variational inequality problem
  • inertial-type algorithm

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