An efficient hybrid conjugate gradient method for unconstrained optimization and image restoration problems
The conjugate gradient (CG) method is an optimization technique known for its rapid convergence; it has blossomed into significant developments and applications. Numerous variations of CG methods have emerged to en-hance computational efficiency and address real-world challenges. In this work, a nov...
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| Format: | Article |
| Language: | English |
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Ferdowsi University of Mashhad
2025-03-01
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| Series: | Iranian Journal of Numerical Analysis and Optimization |
| Subjects: | |
| Online Access: | https://ijnao.um.ac.ir/article_45709_488077f4279cfd491a4cf6e1ba65597e.pdf |
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| author | C. Souli R. Ziadi I. Lakhdari A. Leulmi |
| author_facet | C. Souli R. Ziadi I. Lakhdari A. Leulmi |
| author_sort | C. Souli |
| collection | DOAJ |
| description | The conjugate gradient (CG) method is an optimization technique known for its rapid convergence; it has blossomed into significant developments and applications. Numerous variations of CG methods have emerged to en-hance computational efficiency and address real-world challenges. In this work, a novel conjugate gradient method is introduced to solve nonlinear unconstrained optimization problems. Based on the combination of PRP (Polak–Ribière–Polyak), HRM (Hamoda–Rivaie–Mamat) and NMFR (new modified Fletcher–Reeves) algorithms, our method produces a descent di-rection without depending on any line search. Moreover, it enjoys global convergence under mild assumptions and is applied successfully on various standard test problems as well as image processing. The numerical results indicate that the proposed method outperforms several existing methods in terms of efficiency. |
| format | Article |
| id | doaj-art-deeb2f7fc1924edc875585213a7c9a0b |
| institution | OA Journals |
| issn | 2423-6977 2423-6969 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Ferdowsi University of Mashhad |
| record_format | Article |
| series | Iranian Journal of Numerical Analysis and Optimization |
| spelling | doaj-art-deeb2f7fc1924edc875585213a7c9a0b2025-08-20T02:13:39ZengFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69772423-69692025-03-0115Issue 19912310.22067/ijnao.2024.88087.144945709An efficient hybrid conjugate gradient method for unconstrained optimization and image restoration problemsC. Souli0R. Ziadi1I. Lakhdari2A. Leulmi3Laboratory of Fundamental and Numerical Mathematics (LMFN), University Ferhat Abbas Setif 1, Algeria.Laboratory of Fundamental and Numerical Mathematics (LMFN), University Ferhat Abbas Setif 1, Algeria.Laboratory of Mathematical Analysis, Probability and Optimizations, Biskra University, Algeria.Laboratory of Fundamental and Numerical Mathematics (LMFN), University Ferhat Abbas Setif 1, Algeria.The conjugate gradient (CG) method is an optimization technique known for its rapid convergence; it has blossomed into significant developments and applications. Numerous variations of CG methods have emerged to en-hance computational efficiency and address real-world challenges. In this work, a novel conjugate gradient method is introduced to solve nonlinear unconstrained optimization problems. Based on the combination of PRP (Polak–Ribière–Polyak), HRM (Hamoda–Rivaie–Mamat) and NMFR (new modified Fletcher–Reeves) algorithms, our method produces a descent di-rection without depending on any line search. Moreover, it enjoys global convergence under mild assumptions and is applied successfully on various standard test problems as well as image processing. The numerical results indicate that the proposed method outperforms several existing methods in terms of efficiency.https://ijnao.um.ac.ir/article_45709_488077f4279cfd491a4cf6e1ba65597e.pdfunconstrained optimizationhybrid conjugate gradientglobal convergenceimage restoration |
| spellingShingle | C. Souli R. Ziadi I. Lakhdari A. Leulmi An efficient hybrid conjugate gradient method for unconstrained optimization and image restoration problems Iranian Journal of Numerical Analysis and Optimization unconstrained optimization hybrid conjugate gradient global convergence image restoration |
| title | An efficient hybrid conjugate gradient method for unconstrained optimization and image restoration problems |
| title_full | An efficient hybrid conjugate gradient method for unconstrained optimization and image restoration problems |
| title_fullStr | An efficient hybrid conjugate gradient method for unconstrained optimization and image restoration problems |
| title_full_unstemmed | An efficient hybrid conjugate gradient method for unconstrained optimization and image restoration problems |
| title_short | An efficient hybrid conjugate gradient method for unconstrained optimization and image restoration problems |
| title_sort | efficient hybrid conjugate gradient method for unconstrained optimization and image restoration problems |
| topic | unconstrained optimization hybrid conjugate gradient global convergence image restoration |
| url | https://ijnao.um.ac.ir/article_45709_488077f4279cfd491a4cf6e1ba65597e.pdf |
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