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

Kasamsuk Ungchittrakool; Natthaphon Artsawang; Kasamsuk Ungchittrakool; Natthaphon Artsawang

doi:10.3934/math.20241149

AIMS Mathematics

2024, Volume 9, Issue 9: 23632-23650. doi: 10.3934/math.20241149

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Research article

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

Kasamsuk Ungchittrakool ^1,2,
Natthaphon Artsawang ^{1,2
,
,}

1.
Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
2.
Research Center for Academic Excellence in Nonlinear Analysis and Optimization, Faculty of Science, Phitsanulok 65000, Thailand

Received: 05 May 2024 Revised: 27 July 2024 Accepted: 01 August 2024 Published: 07 August 2024
MSC : 47H04, 47H10, 65K05, 90C25

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.
- inertial method,
- forward-backward algorithm,
- monotone inclusion problem
Citation: Kasamsuk Ungchittrakool, Natthaphon Artsawang. A generalized viscosity forward-backward splitting scheme with inertial terms for solving monotone inclusion problems and its applications[J]. AIMS Mathematics, 2024, 9(9): 23632-23650. doi: 10.3934/math.20241149

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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.

References

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