Global convergence of the Armijo epsilon steepest descent algorithm
In this article, we study the unconstrained minimization problem\[(P)\,\,\,\min\left\{ f(x):x\in\mathbb{R}^{n}\right\} .\]where \(f:\mathbb{R}^{n}\rightarrow\mathbb{R}\) is a continuously differentiable function. We introduce a new algorithm which accelerates the convergence of the steepest descent...
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| Format: | Article |
| Language: | English |
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Publishing House of the Romanian Academy
2012-08-01
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| Series: | Journal of Numerical Analysis and Approximation Theory |
| Subjects: | |
| Online Access: | https://www.ictp.acad.ro/jnaat/journal/article/view/978 |
| _version_ | 1818520933064769536 |
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| author | Nour E. Rahali Nacera Djeghaba Rachid Benzine |
| author_facet | Nour E. Rahali Nacera Djeghaba Rachid Benzine |
| author_sort | Nour E. Rahali |
| collection | DOAJ |
| description | In this article, we study the unconstrained minimization problem\[(P)\,\,\,\min\left\{ f(x):x\in\mathbb{R}^{n}\right\} .\]where \(f:\mathbb{R}^{n}\rightarrow\mathbb{R}\) is a continuously differentiable function. We introduce a new algorithm which accelerates the convergence of the steepest descent method. We further establish the global convergence of this algorithm in the case of Armijo inexact line search. |
| first_indexed | 2024-12-11T01:44:16Z |
| format | Article |
| id | doaj.art-985e5dbd03f54c03b46205537bd91340 |
| institution | Directory Open Access Journal |
| issn | 2457-6794 2501-059X |
| language | English |
| last_indexed | 2024-12-11T01:44:16Z |
| publishDate | 2012-08-01 |
| publisher | Publishing House of the Romanian Academy |
| record_format | Article |
| series | Journal of Numerical Analysis and Approximation Theory |
| spelling | doaj.art-985e5dbd03f54c03b46205537bd913402022-12-22T01:24:56ZengPublishing House of the Romanian AcademyJournal of Numerical Analysis and Approximation Theory2457-67942501-059X2012-08-01412Global convergence of the Armijo epsilon steepest descent algorithmNour E. Rahali0Nacera Djeghaba1Rachid Benzine2Souk Ahras UniversityBadji Mokhtar UniversityBadji Mokhtar UniversityIn this article, we study the unconstrained minimization problem\[(P)\,\,\,\min\left\{ f(x):x\in\mathbb{R}^{n}\right\} .\]where \(f:\mathbb{R}^{n}\rightarrow\mathbb{R}\) is a continuously differentiable function. We introduce a new algorithm which accelerates the convergence of the steepest descent method. We further establish the global convergence of this algorithm in the case of Armijo inexact line search.https://www.ictp.acad.ro/jnaat/journal/article/view/978unconstrained optimizationglobal convergencesteepest descent algorithm\( \varepsilon\)-algorithmArmijo inexact line search |
| spellingShingle | Nour E. Rahali Nacera Djeghaba Rachid Benzine Global convergence of the Armijo epsilon steepest descent algorithm Journal of Numerical Analysis and Approximation Theory unconstrained optimization global convergence steepest descent algorithm \( \varepsilon\)-algorithm Armijo inexact line search |
| title | Global convergence of the Armijo epsilon steepest descent algorithm |
| title_full | Global convergence of the Armijo epsilon steepest descent algorithm |
| title_fullStr | Global convergence of the Armijo epsilon steepest descent algorithm |
| title_full_unstemmed | Global convergence of the Armijo epsilon steepest descent algorithm |
| title_short | Global convergence of the Armijo epsilon steepest descent algorithm |
| title_sort | global convergence of the armijo epsilon steepest descent algorithm |
| topic | unconstrained optimization global convergence steepest descent algorithm \( \varepsilon\)-algorithm Armijo inexact line search |
| url | https://www.ictp.acad.ro/jnaat/journal/article/view/978 |
| work_keys_str_mv | AT nourerahali globalconvergenceofthearmijoepsilonsteepestdescentalgorithm AT naceradjeghaba globalconvergenceofthearmijoepsilonsteepestdescentalgorithm AT rachidbenzine globalconvergenceofthearmijoepsilonsteepestdescentalgorithm |