Strong Convergence of Forward–Reflected–Backward Splitting Methods for Solving Monotone Inclusions with Applications to Image Restoration and Optimal Control

In this paper, we propose and study several strongly convergent versions of the forward–reflected–backward splitting method of Malitsky and Tam for finding a zero of the sum of two monotone operators in a real Hilbert space. Our proposed methods only require one forward evaluation of the single-valu...

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Vydáno v:Journal of scientific computing Ročník 94; číslo 3; s. 73
Hlavní autoři: Izuchukwu, Chinedu, Reich, Simeon, Shehu, Yekini, Taiwo, Adeolu
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.03.2023
Springer Nature B.V
Témata:
Algorithms
Approximation
Computational Mathematics and Numerical Analysis
Convergence
Hilbert space
Image restoration
Inclusions
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Methods
Operators (mathematics)
Optimal control
Optimization
Splitting
Theoretical
Viscosity
Viscosity iteration
Monotone inclusion
Strong convergence
47H10
49J20
Forward–reflected–backward method
49J40
47H09
Halpern’s iteration
Inertial method
ISSN:0885-7474, 1573-7691
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Popis
Shrnutí:In this paper, we propose and study several strongly convergent versions of the forward–reflected–backward splitting method of Malitsky and Tam for finding a zero of the sum of two monotone operators in a real Hilbert space. Our proposed methods only require 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. We also develop inertial versions of our methods and strong convergence results are obtained for these methods when the set-valued operator is maximal monotone and the single-valued operator is Lipschitz continuous and monotone. Finally, we discuss some examples from image restorations and optimal control regarding the implementations of our methods in comparisons with known related methods in the literature.
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ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-023-02132-6