A Combination of Two Conjugate Gradient Methods Under A New Line Search with its Application in Image Restoration Problems
A combined conjugate gradient algorithm is introduced for solving unconstrained optimization problems. In the suggested approach, the conjugate gradient parameter is defined as a combination of PRP (Polak-Ribíere-Polyak) and BRB (Rahali-Belloufi-Benzine) conjugate gradient parameters. To improve the...
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| Language: | English |
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2025-06-01
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| Series: | International Journal of Applied Mathematics and Computer Science |
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| Online Access: | https://doi.org/10.61822/amcs-2025-0019 |
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| author | Maiza Asma Ziadi Raouf Saleh Mohammed A. Almaymuni Abdulgader Z. |
| author_facet | Maiza Asma Ziadi Raouf Saleh Mohammed A. Almaymuni Abdulgader Z. |
| author_sort | Maiza Asma |
| collection | DOAJ |
| description | A combined conjugate gradient algorithm is introduced for solving unconstrained optimization problems. In the suggested approach, the conjugate gradient parameter is defined as a combination of PRP (Polak-Ribíere-Polyak) and BRB (Rahali-Belloufi-Benzine) conjugate gradient parameters. To improve the convergence properties, we have adopted a new inexact line search technique that fits in with the suggested approach. The proposed line search technique can be useful for other gradient descent methods. We have established the existence of a step length that meets the new line search conditions. The generated descent direction and the convergence properties of the suggested approach are studied under the new line search conditions and the proposed method converges globally under mild assumptions. Our approach is evaluated on various test functions, and a comparison with similar recent algorithms is carried out. Furthermore, the proposed algorithm is applied for restoring images with different noise levels. |
| format | Article |
| id | doaj-art-f227e16a474043f5aa9ddcb4d4f15410 |
| institution | Matheson Library |
| issn | 2083-8492 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Sciendo |
| record_format | Article |
| series | International Journal of Applied Mathematics and Computer Science |
| spelling | doaj-art-f227e16a474043f5aa9ddcb4d4f154102025-06-30T06:58:14ZengSciendoInternational Journal of Applied Mathematics and Computer Science2083-84922025-06-0135226728010.61822/amcs-2025-0019A Combination of Two Conjugate Gradient Methods Under A New Line Search with its Application in Image Restoration ProblemsMaiza Asma0Ziadi Raouf1Saleh Mohammed A.2Almaymuni Abdulgader Z.31Laboratory of Fundamental and Numerical Mathematics (LMFN), Department of Mathematics, University Setif-1-Ferhat Abbas, Setif, Algeria1Laboratory of Fundamental and Numerical Mathematics (LMFN), Department of Mathematics, University Setif-1-Ferhat Abbas, Setif, Algeria2Department of Cybersecurity, College of Computer, Qassim University, Saudi Arabia2Department of Cybersecurity, College of Computer, Qassim University, Saudi ArabiaA combined conjugate gradient algorithm is introduced for solving unconstrained optimization problems. In the suggested approach, the conjugate gradient parameter is defined as a combination of PRP (Polak-Ribíere-Polyak) and BRB (Rahali-Belloufi-Benzine) conjugate gradient parameters. To improve the convergence properties, we have adopted a new inexact line search technique that fits in with the suggested approach. The proposed line search technique can be useful for other gradient descent methods. We have established the existence of a step length that meets the new line search conditions. The generated descent direction and the convergence properties of the suggested approach are studied under the new line search conditions and the proposed method converges globally under mild assumptions. Our approach is evaluated on various test functions, and a comparison with similar recent algorithms is carried out. Furthermore, the proposed algorithm is applied for restoring images with different noise levels.https://doi.org/10.61822/amcs-2025-0019unconstrained optimizationconjugate gradient methodsinexact line searchglobal convergenceimage processing |
| spellingShingle | Maiza Asma Ziadi Raouf Saleh Mohammed A. Almaymuni Abdulgader Z. A Combination of Two Conjugate Gradient Methods Under A New Line Search with its Application in Image Restoration Problems International Journal of Applied Mathematics and Computer Science unconstrained optimization conjugate gradient methods inexact line search global convergence image processing |
| title | A Combination of Two Conjugate Gradient Methods Under A New Line Search with its Application in Image Restoration Problems |
| title_full | A Combination of Two Conjugate Gradient Methods Under A New Line Search with its Application in Image Restoration Problems |
| title_fullStr | A Combination of Two Conjugate Gradient Methods Under A New Line Search with its Application in Image Restoration Problems |
| title_full_unstemmed | A Combination of Two Conjugate Gradient Methods Under A New Line Search with its Application in Image Restoration Problems |
| title_short | A Combination of Two Conjugate Gradient Methods Under A New Line Search with its Application in Image Restoration Problems |
| title_sort | combination of two conjugate gradient methods under a new line search with its application in image restoration problems |
| topic | unconstrained optimization conjugate gradient methods inexact line search global convergence image processing |
| url | https://doi.org/10.61822/amcs-2025-0019 |
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