Two-step inertial forward–reflected–anchored–backward splitting algorithm for solving monotone inclusion problems

The main purpose of this paper is to propose and study a two-step inertial anchored version of the forward–reflected–backward splitting algorithm of Malitsky and Tam in a real Hilbert space. Our proposed algorithm converges strongly to a zero of the sum of a set-valued maximal monotone operator and...

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Bibliographic Details
Published in:Computational & applied mathematics Vol. 42; no. 8
Main Authors: Izuchukwu, Chinedu, Aphane, Maggie, Aremu, Kazeem Olalekan
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.12.2023
Subjects:
Applications of Mathematics
Computational Mathematics and Numerical Analysis
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Monotone inclusion
Strong convergence
47H10
49J20
Forward–reflected–backward method
49J40
47H09
Halpern’s iteration
Two-step inertial
ISSN:2238-3603, 1807-0302
Online Access:Get full text
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Summary:The main purpose of this paper is to propose and study a two-step inertial anchored version of the forward–reflected–backward splitting algorithm of Malitsky and Tam in a real Hilbert space. Our proposed algorithm converges strongly to a zero of the sum of a set-valued maximal monotone operator and a single-valued monotone Lipschitz continuous operator. It involves only one forward evaluation of the single-valued operator and one backward evaluation of the set-valued operator at each iteration; a feature that is absent in many other available strongly convergent splitting methods in the literature. Finally, we perform numerical experiments involving image restoration problem and compare our algorithm with known related strongly convergent splitting algorithms in the literature.
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-023-02485-6