A generalized viscosity forward-backward splitting scheme with inertial terms for solving monotone inclusion problems and its applications

Our aim was to establish a novel generalized viscosity forward-backward splitting scheme that incorporates inertial terms for addressing monotone inclusion problems within a Hilbert space. By incorporating appropriate control conditions, we achieved strong convergence. The significance of this theor...

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Vydáno v:AIMS mathematics Ročník 9; číslo 9; s. 23632 - 23650
Hlavní autoři: Ungchittrakool, Kasamsuk, Artsawang, Natthaphon
Médium: Journal Article
Jazyk:angličtina
Vydáno: AIMS Press 01.01.2024
Témata:
forward-backward algorithm
inertial method
monotone inclusion problem
ISSN:2473-6988, 2473-6988
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Abstract Our aim was to establish a novel generalized viscosity forward-backward splitting scheme that incorporates inertial terms for addressing monotone inclusion problems within a Hilbert space. By incorporating appropriate control conditions, we achieved strong convergence. The significance of this theorem lies in its applicability to resolve convex minimization problems. To demonstrate the efficacy of our proposed algorithm, we conducted a comparative analysis of its convergence behavior against other algorithms. Finally, we showcased the performance of our proposed method through numerical experiments aimed at addressing image restoration problems.
AbstractList Our aim was to establish a novel generalized viscosity forward-backward splitting scheme that incorporates inertial terms for addressing monotone inclusion problems within a Hilbert space. By incorporating appropriate control conditions, we achieved strong convergence. The significance of this theorem lies in its applicability to resolve convex minimization problems. To demonstrate the efficacy of our proposed algorithm, we conducted a comparative analysis of its convergence behavior against other algorithms. Finally, we showcased the performance of our proposed method through numerical experiments aimed at addressing image restoration problems.
Author Artsawang, Natthaphon
Ungchittrakool, Kasamsuk
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SubjectTerms forward-backward algorithm
inertial method
monotone inclusion problem
Title A generalized viscosity forward-backward splitting scheme with inertial terms for solving monotone inclusion problems and its applications
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