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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| Vydáno v: | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Ročník 114; číslo 2 |
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Springer International Publishing
01.04.2020
Springer Nature B.V |
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| ISSN: | 1578-7303, 1579-1505 |
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| Abstract | 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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| AbstractList | 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. |
| ArticleNumber | 99 |
| Author | Yambangwai, Damrongsak Cholamjiak, Watcharaporn Khan, Suhel Ahmad Kazmi, Kaleem Raza |
| Author_xml | – sequence: 1 givenname: Watcharaporn surname: Cholamjiak fullname: Cholamjiak, Watcharaporn organization: School of Science, University of Phayao – sequence: 2 givenname: Suhel Ahmad surname: Khan fullname: Khan, Suhel Ahmad email: khan.math@gmail.com organization: Department of Mathematics, BITS-Pilani – sequence: 3 givenname: Damrongsak surname: Yambangwai fullname: Yambangwai, Damrongsak organization: School of Science, University of Phayao – sequence: 4 givenname: Kaleem Raza surname: Kazmi fullname: Kazmi, Kaleem Raza organization: Department of Mathematics, Faculty of Science and Arts–Rabigh, King Abdulaziz University |
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| Keywords | Parallel monotone hybrid algorithms 47H10 49M30 46T99 Common variational inclusion problems Inertial methods Fixed point problems 49M37 47H05 47J25 Forward-backward algorithms |
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| SubjectTerms | Algorithms Applications of Mathematics Convergence Hilbert space Image restoration Mathematical and Computational Physics Mathematics Mathematics and Statistics Original Paper Theoretical |
| Title | Strong convergence analysis of common variational inclusion problems involving an inertial parallel monotone hybrid method for a novel application to image restoration |
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