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

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 prob...

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Bibliographic Details
Published in:Resultate der Mathematik Vol. 75; no. 4
Main Authors: Gibali, Aviv, Jolaoso, Lateef Olakunle, Mewomo, Oluwatosin Temitope, Taiwo, Adeolu
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.12.2020
Subjects:
Mathematics
Mathematics and Statistics
Bregman weak relatively nonexpansive mappings
47H10
90C33
Variational inequality problem
Banach spaces
47J25
47N10
inertial-type algorithm
65J15
ISSN:1422-6383, 1420-9012
Online Access:Get full text
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Summary: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.
ISSN:1422-6383
1420-9012
DOI:10.1007/s00025-020-01306-0