Nonlinear Conjugate Gradient Coefficients with Exact and Strong Wolfe Line Searches Techniques
Nonlinear conjugate gradient (CG) methods are very important for solving unconstrained optimization problems. These methods have been subjected to extensive researches in terms of enhancing them. Exact and strong Wolfe line search techniques are usually used in practice for the analysis and implemen...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/1383129 |
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| author | Awad Abdelrahman Mogtaba Mohammed Osman O. O. Yousif Murtada K. Elbashir |
| author_facet | Awad Abdelrahman Mogtaba Mohammed Osman O. O. Yousif Murtada K. Elbashir |
| author_sort | Awad Abdelrahman |
| collection | DOAJ |
| description | Nonlinear conjugate gradient (CG) methods are very important for solving unconstrained optimization problems. These methods have been subjected to extensive researches in terms of enhancing them. Exact and strong Wolfe line search techniques are usually used in practice for the analysis and implementation of conjugate gradient methods. For better results, several studies have been carried out to modify classical CG methods. The method of Fletcher and Reeves (FR) is one of the most well-known CG methods. It has strong convergence properties, but it gives poor numerical results in practice. The main goal of this paper is to enhance this method in terms of numerical performance via a convexity type of modification on its coefficient βk. We ensure that with this modification, the method is still achieving the sufficient descent condition and global convergence via both exact and strong Wolfe line searches. The numerical results show that this modified FR is more robust and effective. |
| format | Article |
| id | doaj-art-a7581cd6d084447ea5046edf15c94803 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-a7581cd6d084447ea5046edf15c948032025-02-03T06:13:04ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/1383129Nonlinear Conjugate Gradient Coefficients with Exact and Strong Wolfe Line Searches TechniquesAwad Abdelrahman0Mogtaba Mohammed1Osman O. O. Yousif2Murtada K. Elbashir3Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of Information SystemsNonlinear conjugate gradient (CG) methods are very important for solving unconstrained optimization problems. These methods have been subjected to extensive researches in terms of enhancing them. Exact and strong Wolfe line search techniques are usually used in practice for the analysis and implementation of conjugate gradient methods. For better results, several studies have been carried out to modify classical CG methods. The method of Fletcher and Reeves (FR) is one of the most well-known CG methods. It has strong convergence properties, but it gives poor numerical results in practice. The main goal of this paper is to enhance this method in terms of numerical performance via a convexity type of modification on its coefficient βk. We ensure that with this modification, the method is still achieving the sufficient descent condition and global convergence via both exact and strong Wolfe line searches. The numerical results show that this modified FR is more robust and effective.http://dx.doi.org/10.1155/2022/1383129 |
| spellingShingle | Awad Abdelrahman Mogtaba Mohammed Osman O. O. Yousif Murtada K. Elbashir Nonlinear Conjugate Gradient Coefficients with Exact and Strong Wolfe Line Searches Techniques Journal of Mathematics |
| title | Nonlinear Conjugate Gradient Coefficients with Exact and Strong Wolfe Line Searches Techniques |
| title_full | Nonlinear Conjugate Gradient Coefficients with Exact and Strong Wolfe Line Searches Techniques |
| title_fullStr | Nonlinear Conjugate Gradient Coefficients with Exact and Strong Wolfe Line Searches Techniques |
| title_full_unstemmed | Nonlinear Conjugate Gradient Coefficients with Exact and Strong Wolfe Line Searches Techniques |
| title_short | Nonlinear Conjugate Gradient Coefficients with Exact and Strong Wolfe Line Searches Techniques |
| title_sort | nonlinear conjugate gradient coefficients with exact and strong wolfe line searches techniques |
| url | http://dx.doi.org/10.1155/2022/1383129 |
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