The Modified Viscosity Approximation Method with Inertial Technique and Forward–Backward Algorithm for Convex Optimization Model
In this paper, we propose a new accelerated algorithm for finding a common fixed point of nonexpansive operators, and then, a strong convergence result of the proposed method is discussed and analyzed in real Hilbert spaces. As an application, we create a new accelerated viscosity forward–backward m...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/7/1036 |
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| author | Adisak Hanjing Limpapat Bussaban Suthep Suantai |
| author_facet | Adisak Hanjing Limpapat Bussaban Suthep Suantai |
| author_sort | Adisak Hanjing |
| collection | DOAJ |
| description | In this paper, we propose a new accelerated algorithm for finding a common fixed point of nonexpansive operators, and then, a strong convergence result of the proposed method is discussed and analyzed in real Hilbert spaces. As an application, we create a new accelerated viscosity forward–backward method (AVFBM) for solving nonsmooth optimization problems of the sum of two objective functions in real Hilbert spaces, and the strong convergence of AVFBM to a minimizer of the sum of two convex functions is established. We also present the application and simulated results of AVFBM for image restoration and data classification problems. |
| first_indexed | 2024-03-09T11:39:21Z |
| format | Article |
| id | doaj.art-891c28c5c4414386ac5d0c968c73542a |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T11:39:21Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-891c28c5c4414386ac5d0c968c73542a2023-11-30T23:36:14ZengMDPI AGMathematics2227-73902022-03-01107103610.3390/math10071036The Modified Viscosity Approximation Method with Inertial Technique and Forward–Backward Algorithm for Convex Optimization ModelAdisak Hanjing0Limpapat Bussaban1Suthep Suantai2Department of Science and Mathematics, Rajamangala University of Technology Isan Surin Campus, Surin 32000, ThailandFaculty of Science, Chiang Mai University, Chiang Mai 50200, ThailandData Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, ThailandIn this paper, we propose a new accelerated algorithm for finding a common fixed point of nonexpansive operators, and then, a strong convergence result of the proposed method is discussed and analyzed in real Hilbert spaces. As an application, we create a new accelerated viscosity forward–backward method (AVFBM) for solving nonsmooth optimization problems of the sum of two objective functions in real Hilbert spaces, and the strong convergence of AVFBM to a minimizer of the sum of two convex functions is established. We also present the application and simulated results of AVFBM for image restoration and data classification problems.https://www.mdpi.com/2227-7390/10/7/1036Hilbert spacecommon fixed pointsviscosity forward–backward algorithmconvergence theoremsconvex optimization model |
| spellingShingle | Adisak Hanjing Limpapat Bussaban Suthep Suantai The Modified Viscosity Approximation Method with Inertial Technique and Forward–Backward Algorithm for Convex Optimization Model Mathematics Hilbert space common fixed points viscosity forward–backward algorithm convergence theorems convex optimization model |
| title | The Modified Viscosity Approximation Method with Inertial Technique and Forward–Backward Algorithm for Convex Optimization Model |
| title_full | The Modified Viscosity Approximation Method with Inertial Technique and Forward–Backward Algorithm for Convex Optimization Model |
| title_fullStr | The Modified Viscosity Approximation Method with Inertial Technique and Forward–Backward Algorithm for Convex Optimization Model |
| title_full_unstemmed | The Modified Viscosity Approximation Method with Inertial Technique and Forward–Backward Algorithm for Convex Optimization Model |
| title_short | The Modified Viscosity Approximation Method with Inertial Technique and Forward–Backward Algorithm for Convex Optimization Model |
| title_sort | modified viscosity approximation method with inertial technique and forward backward algorithm for convex optimization model |
| topic | Hilbert space common fixed points viscosity forward–backward algorithm convergence theorems convex optimization model |
| url | https://www.mdpi.com/2227-7390/10/7/1036 |
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