Self-adaptive forward–backward splitting algorithm for the sum of two monotone operators in Banach spaces

In this work, we prove the weak convergence of a one-step self-adaptive algorithm to a solution of the sum of two monotone operators in 2-uniformly convex and uniformly smooth real Banach spaces. We give numerical examples in infinite-dimensional spaces to compare our result with some existing algor...

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Bibliographic Details
Published in:Fixed point theory and algorithms for sciences and engineering Vol. 2022; no. 1; pp. 1 - 16
Main Authors: Bello, Abdulmalik U., Chidume, Charles E., Alka, Maryam
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 06.12.2022
Springer Nature B.V
SpringerOpen
Subjects:
2-uniformly convex spaces
Adaptive algorithms
Algorithms
Analysis
Applications of Mathematics
Banach spaces
Differential Geometry
Forward–reflected–backward splitting method
Lipschitz-continuous operator
Machine learning
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Maximal monotone operators
Operators
Topology
47H10
Maximal monotone operators
49J20
49J40
2-uniformly convex spaces
47H09
Forward–reflected–backward splitting method
Lipschitz-continuous operator
ISSN:2730-5422, 2730-5422
Online Access:Get full text
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Summary:In this work, we prove the weak convergence of a one-step self-adaptive algorithm to a solution of the sum of two monotone operators in 2-uniformly convex and uniformly smooth real Banach spaces. We give numerical examples in infinite-dimensional spaces to compare our result with some existing algorithms. Finally, our results extend and complement several existing results in the literature.
Bibliography:ObjectType-Article-1
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ISSN:2730-5422
2730-5422
DOI:10.1186/s13663-022-00732-9