Strong convergence analysis of common variational inclusion problems involving an inertial parallel monotone hybrid method for a novel application to image restoration

In this paper, we propose inertial forward-backward splitting algorithm to approximate the solution of common variational inclusion problems. By using the inertial technique with parallel monotone hybrid methods we prove strong convergence results under some suitable conditions in Hilbert spaces. We...

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Bibliographic Details
Published in:Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Vol. 114; no. 2
Main Authors: Cholamjiak, Watcharaporn, Khan, Suhel Ahmad, Yambangwai, Damrongsak, Kazmi, Kaleem Raza
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.04.2020
Springer Nature B.V
Subjects:
Algorithms
Applications of Mathematics
Convergence
Hilbert space
Image restoration
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Original Paper
Theoretical
Parallel monotone hybrid algorithms
47H10
49M30
46T99
Common variational inclusion problems
Inertial methods
Fixed point problems
49M37
47H05
47J25
Forward-backward algorithms
ISSN:1578-7303, 1579-1505
Online Access:Get full text
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Summary:In this paper, we propose inertial forward-backward splitting algorithm to approximate the solution of common variational inclusion problems. By using the inertial technique with parallel monotone hybrid methods we prove strong convergence results under some suitable conditions in Hilbert spaces. We then give some applications and numerical experiments for supporting our main results which shows that our proposed inertial hybrid method has better convergence rate than existing algorithms. Further, we apply our result to solve a common convex minimization problem and a common split feasibility problem. Finally, we use our proposed algorithm to solve the unconstrained image restoration problems and we can show that our algorithm is flexibility and good quality to use for common types of blur effects.
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ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-020-00827-1