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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Bibliographic Details
Published in:	AIMS mathematics Vol. 9; no. 9; pp. 23632 - 23650
Main Authors:	Ungchittrakool, Kasamsuk, Artsawang, Natthaphon
Format:	Journal Article
Language:	English
Published:	AIMS Press 01.01.2024
Subjects:	forward-backward algorithm inertial method monotone inclusion problem
ISSN:	2473-6988, 2473-6988
Online Access:	Get full text
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Summary:	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.
ISSN:	2473-6988 2473-6988
DOI:	10.3934/math.20241149