An efficient iterative method for solving split variational inclusion problem with applications

Jamilu Abubakar; Poom Kumam; Abor Isa Garba; Muhammad Sirajo Abdullahi; Abdulkarim Hassan Ibrahim; Wachirapong Jirakitpuwapat

doi:10.3934/jimo.2021160

Article Contents

2022, Volume 18, Issue 6: 4311-4331. Doi: 10.3934/jimo.2021160

This issue Previous Article Outsourcing contract design for the green transformation of manufacturing systems under asymmetric information Next Article A study on vector variational-like inequalities using convexificators and application to its bi-level form

An efficient iterative method for solving split variational inclusion problem with applications

1.
Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangkok 10140, Thailand
2.
Department of Mathematics, Faculty of Science, Usmanu Danfodiyo University, Sokoto 840244, Nigeria
3.
Departments of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan

^* Corresponding author: poom.kum@kmutt.ac.th
^* Corresponding author: poom.kum@kmutt.ac.th

Received: October 2020

Revised: May 2021

Early access: September 2021

Published: September 2022

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Abstract

A new strong convergence iterative method for solving a split variational inclusion problem involving a bounded linear operator and two maximally monotone mappings is proposed in this article. The study considers an iterative scheme comprised of inertial extrapolation step together with the Mann-type step. A strong convergence theorem of the iterates generated by the proposed iterative scheme is given under suitable conditions. In addition, methods for solving variational inequality problems and split convex feasibility problems are derived from the proposed method. Applications of solving Nash-equilibrium problems and image restoration problems are solved using the derived methods to demonstrate the implementation of the proposed methods. Numerical comparisons with some existing iterative methods are also presented.

Keywords:

Mathematics Subject Classification: Primary: 47H05, 47J20, 47J25; Secondary: 65K15.

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Figure 1. Comparative results for random instances.

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Figure 2. Results of the compared algorithms with different cases of initial points.

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Figure 3. Original test images of Monarch, Flowers and Colorchecker.

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Figure 4. Original cropped test images of Monarch, Flowers and Colorchecker.

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Figure 5. Degraded and restored Monarch images by the compared algorithms.

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Figure 6. Degraded and restored cropped Monarch images by the compared algorithms.

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Figure 7. Degraded and restored Flowers images by the compared algorithms.

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Figure 8. Degraded and restored cropped Flowers images by the compared algorithms.

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Figure 9. Degraded and restored Colorchecker images by the compared algorithms.

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Figure 10. Degraded and restored cropped Colorchecker images by the compared algorithms.

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Table 1. The PNSR and SSIM values of the compared algorithms

	Scheme 51		Algorithm 4.4
Images	SNR	SSIM	SNR	SSIM
Monarch	43.3255	0.9684	39.5788	0.9624
Flowers	40.6001	0.9116	36.7745	0.8660
Colorchecker	41.7454	0.8996	39.0134	0.9061

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