A Modified Liu and Storey Conjugate Gradient Method for Large Scale Unconstrained Optimization Problems
The conjugate gradient method is one of the most popular methods to solve large-scale unconstrained optimization problems since it does not require the second derivative, such as Newton’s method or approximations. Moreover, the conjugate gradient method can be applied in many fields such as neural n...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-07-01
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| Series: | Algorithms |
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| Online Access: | https://www.mdpi.com/1999-4893/14/8/227 |
| _version_ | 1797524963914153984 |
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| author | Zabidin Salleh Ghaliah Alhamzi Ibitsam Masmali Ahmad Alhawarat |
| author_facet | Zabidin Salleh Ghaliah Alhamzi Ibitsam Masmali Ahmad Alhawarat |
| author_sort | Zabidin Salleh |
| collection | DOAJ |
| description | The conjugate gradient method is one of the most popular methods to solve large-scale unconstrained optimization problems since it does not require the second derivative, such as Newton’s method or approximations. Moreover, the conjugate gradient method can be applied in many fields such as neural networks, image restoration, etc. Many complicated methods are proposed to solve these optimization functions in two or three terms. In this paper, we propose a simple, easy, efficient, and robust conjugate gradient method. The new method is constructed based on the Liu and Storey method to overcome the convergence problem and descent property. The new modified method satisfies the convergence properties and the sufficient descent condition under some assumptions. The numerical results show that the new method outperforms famous CG methods such as CG-Descent 5.3, Liu and Storey, and Dai and Liao. The numerical results include the number of iterations and CPU time. |
| first_indexed | 2024-03-10T09:05:04Z |
| format | Article |
| id | doaj.art-304047acc3ef400781c7c95969b5dc0a |
| institution | Directory Open Access Journal |
| issn | 1999-4893 |
| language | English |
| last_indexed | 2024-03-10T09:05:04Z |
| publishDate | 2021-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj.art-304047acc3ef400781c7c95969b5dc0a2023-11-22T06:27:35ZengMDPI AGAlgorithms1999-48932021-07-0114822710.3390/a14080227A Modified Liu and Storey Conjugate Gradient Method for Large Scale Unconstrained Optimization ProblemsZabidin Salleh0Ghaliah Alhamzi1Ibitsam Masmali2Ahmad Alhawarat3Department of Mathematics, Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, Kuala Nerus 21030, Terengganu, MalaysiaDepartment of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi ArabiaDepartment of Mathematics, College of Science, Jazan University, Jazan 45142, Saudi ArabiaDepartment of Mathematics, Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, Kuala Nerus 21030, Terengganu, MalaysiaThe conjugate gradient method is one of the most popular methods to solve large-scale unconstrained optimization problems since it does not require the second derivative, such as Newton’s method or approximations. Moreover, the conjugate gradient method can be applied in many fields such as neural networks, image restoration, etc. Many complicated methods are proposed to solve these optimization functions in two or three terms. In this paper, we propose a simple, easy, efficient, and robust conjugate gradient method. The new method is constructed based on the Liu and Storey method to overcome the convergence problem and descent property. The new modified method satisfies the convergence properties and the sufficient descent condition under some assumptions. The numerical results show that the new method outperforms famous CG methods such as CG-Descent 5.3, Liu and Storey, and Dai and Liao. The numerical results include the number of iterations and CPU time.https://www.mdpi.com/1999-4893/14/8/227conjugate gradientinexact line searchdescent condition |
| spellingShingle | Zabidin Salleh Ghaliah Alhamzi Ibitsam Masmali Ahmad Alhawarat A Modified Liu and Storey Conjugate Gradient Method for Large Scale Unconstrained Optimization Problems Algorithms conjugate gradient inexact line search descent condition |
| title | A Modified Liu and Storey Conjugate Gradient Method for Large Scale Unconstrained Optimization Problems |
| title_full | A Modified Liu and Storey Conjugate Gradient Method for Large Scale Unconstrained Optimization Problems |
| title_fullStr | A Modified Liu and Storey Conjugate Gradient Method for Large Scale Unconstrained Optimization Problems |
| title_full_unstemmed | A Modified Liu and Storey Conjugate Gradient Method for Large Scale Unconstrained Optimization Problems |
| title_short | A Modified Liu and Storey Conjugate Gradient Method for Large Scale Unconstrained Optimization Problems |
| title_sort | modified liu and storey conjugate gradient method for large scale unconstrained optimization problems |
| topic | conjugate gradient inexact line search descent condition |
| url | https://www.mdpi.com/1999-4893/14/8/227 |
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