2019_Extensions Of Rivaie-Mustafa-Ismail-Leong+ And Fletcher-Reeves Methods For Unconstrained Optimization Problems
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| country | Malaysia |
| date | 2019-07-22 |
| format | General Document |
| id | 16192 |
| institution | UniSZA |
| originalfilename | 16192_319846b79679ba2.pdf |
| person | Abba Vulngwe Mandara |
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| resourceurl | https://intelek.unisza.edu.my/intelek/pages/view.php?ref=16192 |
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| spelling | 16192 https://intelek.unisza.edu.my/intelek/pages/view.php?ref=16192 https://intelek.unisza.edu.my/intelek/pages/search.php?search=!collection3 General Document Malaysia Library Staff (Top Management) Library Staff (Management) Library Staff (Support) Terengganu Faculty of Informatics & Computing English application/pdf 1.5 Server storage Scanned document Universiti Sultan Zainal Abidin UniSZA Private Access UNIVERSITI SULTAN ZAINAL ABIDIN SAMBox 2.3.4; modified using iTextSharp™ 5.5.10 ©2000-2016 iText Group NV (AGPL-version) 226 Copyright©PWB2025 2019-07-22 Conjugate gradient methods 16192_319846b79679ba2.pdf Abba Vulngwe Mandara 2019_Extensions Of Rivaie-Mustafa-Ismail-Leong+ And Fletcher-Reeves Methods For Unconstrained Optimization Problems The Rivaie-Mustafa-Ismail-Leong+ (RMIL+) and Fletcher-Reeves (FR) methods are the prominent methods for solving unconstrained optimization problems. However, these methods do have some shortcomings which include weak global convergence, low-performance in terms of a number of iterations and the Central Processing Unit (CPU) time. The newly introduced methods, Mandara-Mamat-Waziri-Afandee (MMWA) and Mandara-Mamat-Waziri-Usman (MMWU) through modifications have improved the performance of RMIL+ and FR methods using exact line search procedure. To overcome these shortcomings, we proposed an extensions of RMIL+ and FR methods for solving unconstrained optimization problems. These methods required only first order derivative, which leads to the reduction of weak global convergence and low-performance in solving large-scale problems. The methods are obtained through modifications of the numerator of RMIL+ method and retained the denominator. While the denominator in the FR method are modified and retained its numerator. The numerical results are based on the number of iterations and CPU time. The code for the proposed methods was done using MATLAB version, R2012b subroutine programming environment and run on a personal computer 2.4GHz, Intel (R) Core™ i7-5500U CPU processor, 4GB RAM and on Windows 7 operating system. However, for each standard test problem functions, four different arbitrary initial points in the set of real numbers are used, based on the point that are nearest to the solution. The numerical results are analyzed using the performance profile introduced by Dolan and More. The proposed methods are found to be efficient and reliable in terms of the number of iterations and CPU time. The new MMWA and MMWU methods have satisfied the sufficient descent and global convergence properties under appropriate conditions. Hence, these methods are found to be very attractive, especially for large scale optimization problems. Also, the efficiency of the new methods in terms of the percentage are 99.53% higher as compared to RMIL+ method with 82.93%, and FR method with 81.58% respectively. The numerical results show that the proposed methods are reliable, efficient, and effective compared to RMIL+ and FR methods. Thus, the new methods are a good alternative for solving unconstrained optimization problems. Dissertations, Academic Fletcher-Reeves Method Conjugate Gradient Methods Rivaie-Mustafa-Ismail-Leong Method Thesis |
| spellingShingle | 2019_Extensions Of Rivaie-Mustafa-Ismail-Leong+ And Fletcher-Reeves Methods For Unconstrained Optimization Problems |
| state | Terengganu |
| subject | Conjugate gradient methods Dissertations, Academic |
| summary | The Rivaie-Mustafa-Ismail-Leong+ (RMIL+) and Fletcher-Reeves (FR) methods are the prominent methods for solving unconstrained optimization problems. However, these methods do have some shortcomings which include weak global convergence, low-performance in terms of a number of iterations and the Central Processing Unit (CPU) time. The newly introduced methods, Mandara-Mamat-Waziri-Afandee (MMWA) and Mandara-Mamat-Waziri-Usman (MMWU) through modifications have improved the performance of RMIL+ and FR methods using exact line search procedure. To overcome these shortcomings, we proposed an extensions of RMIL+ and FR methods for solving unconstrained optimization problems. These methods required only first order derivative, which leads to the reduction of weak global convergence and low-performance in solving large-scale problems. The methods are obtained through modifications of the numerator of RMIL+ method and retained the denominator. While the denominator in the FR method are modified and retained its numerator. The numerical results are based on the number of iterations and CPU time. The code for the proposed methods was done using MATLAB version, R2012b subroutine programming environment and run on a personal computer 2.4GHz, Intel (R) Core™ i7-5500U CPU processor, 4GB RAM and on Windows 7 operating system. However, for each standard test problem functions, four different arbitrary initial points in the set of real numbers are used, based on the point that are nearest to the solution. The numerical results are analyzed using the performance profile introduced by Dolan and More. The proposed methods are found to be efficient and reliable in terms of the number of iterations and CPU time. The new MMWA and MMWU methods have satisfied the sufficient descent and global convergence properties under appropriate conditions. Hence, these methods are found to be very attractive, especially for large scale optimization problems. Also, the efficiency of the new methods in terms of the percentage are 99.53% higher as compared to RMIL+ method with 82.93%, and FR method with 81.58% respectively. The numerical results show that the proposed methods are reliable, efficient, and effective compared to RMIL+ and FR methods. Thus, the new methods are a good alternative for solving unconstrained optimization problems. |
| title | 2019_Extensions Of Rivaie-Mustafa-Ismail-Leong+ And Fletcher-Reeves Methods For Unconstrained Optimization Problems |
| title_full | 2019_Extensions Of Rivaie-Mustafa-Ismail-Leong+ And Fletcher-Reeves Methods For Unconstrained Optimization Problems |
| title_fullStr | 2019_Extensions Of Rivaie-Mustafa-Ismail-Leong+ And Fletcher-Reeves Methods For Unconstrained Optimization Problems |
| title_full_unstemmed | 2019_Extensions Of Rivaie-Mustafa-Ismail-Leong+ And Fletcher-Reeves Methods For Unconstrained Optimization Problems |
| title_short | 2019_Extensions Of Rivaie-Mustafa-Ismail-Leong+ And Fletcher-Reeves Methods For Unconstrained Optimization Problems |
| title_sort | 2019_extensions of rivaie-mustafa-ismail-leong+ and fletcher-reeves methods for unconstrained optimization problems |