2020_Modified Spectral Conjugate Gradient Methods For Unconstrained Optimization and System of Linear Equations
| Format: | General Document |
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| collectionurl | https://intelek.unisza.edu.my/intelek/pages/search.php?search=!collection3 |
| copyright | Copyright©PWB2025 |
| country | Malaysia |
| date | 2020-08-30 |
| format | General Document |
| id | 16206 |
| institution | UniSZA |
| originalfilename | MODIFIED SPECTRAL CONJUGATE GRADIENT METHODS FOR UNCONSTRAINED OPTIMIZATION AND SYSTEM OF LINEAR EQUATIONS.pdf |
| person | Wan Khadijah Binti Wan Sulaiman |
| recordtype | oai_dc |
| resourceurl | https://intelek.unisza.edu.my/intelek/pages/view.php?ref=16206 |
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| spelling | 16206 https://intelek.unisza.edu.my/intelek/pages/view.php?ref=16206 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 2.4.24; modified using iTextSharp™ 5.5.10 ©2000-2016 iText Group NV (AGPL-version) Copyright©PWB2025 Conjugate gradient methods 2020-08-30 275 MODIFIED SPECTRAL CONJUGATE GRADIENT METHODS FOR UNCONSTRAINED OPTIMIZATION AND SYSTEM OF LINEAR EQUATIONS.pdf Wan Khadijah Binti Wan Sulaiman 2020_Modified Spectral Conjugate Gradient Methods For Unconstrained Optimization and System of Linear Equations Conjugate gradient (CG) method is widely applied for solving large-scale unconstrained optimization. However, some of the improvised CG methods are not applicable to be applied when the CG coefficients formula (pp) involve with parameters. Therefore, this research proposes two modified CG methods to overcome the problems in CG methods. In this research, lwo new spectral CG methods for solving large-scale unconstrained problems are proposed which combine the advantages of spectral CG method and the already proven CG method. The newly proposed methods are based on the two versions of Rivaie-Mustafa-lsmail-Leong (RMIL and RMIL2). Thus, by modifying RMIL and RMIL2 methods, the modified methods are known as MRMIL and MRMIL2. Then, these methods are compared with other CG methods such as Fletcher and Reeve (FR), modified Conjugate Descent (MCD), modified Polak, Ribidre and Polyak (MPRP), and modified Liu and Storey (MLS). Theoretically, the global convergence of the proposed methods has been established using inexact strong-Wolfe line search under standard conditions. The MRMIL and MRMIL2 methods are reduced to the original classical CG methods if an exact line search is applied. Both methods have been tested via Matlab R20l5a programming on twenty three standard optimization problems. Four different initial points are selected, ranging from those near the solution point to the ones far from it. The numerical results are measured based on number of iteration and Central Processing Unit (CPU) time and then analyzed using performance profile. The best method is characterized by the one with the least number of iteration and lower CPU time. The MRMIL and MRMIL2 also have been applied in systems of linear equations for solving large scale matrix problems. Both MRMIL and MRMIL2 methods are theoretically proven to satisf, the sufficient descent and global convergence properties. From the obtained results, the MRMIL2 and MLS methods show the highest percentage of successfully solving the test problems, which are 98.39%. Meanwhile, the MPRP, MRMIL, MCD and MFR methods able to solve 97.04%,96.51%,86.02% and85.75% ofthe standard optimization problems, respectively. Both new methods converge faster and have good performance compared to the other methods. Based on the numerical results, the proposed melhods proven to converge globally thus supporting the theoretical proofs. The finding shows the MRMIL2 method is better than other CG methods. Meanwhile, MRMIL places the third after MLS and MPRP with the difference of 1.88% and 0.53% respectively. Additionally, the numerical results based on relative error also show that the MRMIL and MRMIL2 CG methods are comparable with other CG methods when they are applied in system of linear equations, that are 5.8651x 10-5 and 5.8591x 10-6, respectively. As a conclusion, the MRMIL and MRMIL2 have capabilities for solving unconstrained optimization problems and systems oflinear equations that are competitive with other CG methods. Dissertations, Academic Unconstrained Optimization Conjugate Gradient Algorithm Spectral Conjugate Gradient Methods Thesis |
| spellingShingle | 2020_Modified Spectral Conjugate Gradient Methods For Unconstrained Optimization and System of Linear Equations |
| state | Terengganu |
| subject | Conjugate gradient methods Dissertations, Academic |
| summary | Conjugate gradient (CG) method is widely applied for solving large-scale unconstrained optimization. However, some of the improvised CG methods are not applicable to be applied when the CG coefficients formula (pp) involve with parameters. Therefore, this research proposes two modified CG methods to overcome the problems in CG methods. In this research, lwo new spectral CG methods for solving large-scale unconstrained problems are proposed which combine the advantages of spectral CG method and the already proven CG method. The newly proposed methods are based on the two versions of Rivaie-Mustafa-lsmail-Leong (RMIL and RMIL2). Thus, by modifying RMIL and RMIL2 methods, the modified methods are known as MRMIL and MRMIL2. Then, these methods are compared with other CG methods such as Fletcher and Reeve (FR), modified Conjugate Descent (MCD), modified Polak, Ribidre and Polyak (MPRP), and modified Liu and Storey (MLS). Theoretically, the global convergence of the proposed methods has been established using inexact strong-Wolfe line search under standard conditions. The MRMIL and MRMIL2 methods are reduced to the original classical CG methods if an exact line search is applied. Both methods have been tested via Matlab R20l5a programming on twenty three standard optimization problems. Four different initial points are selected, ranging from those near the solution point to the ones far from it. The numerical results are measured based on number of iteration and Central Processing Unit (CPU) time and then analyzed using performance profile. The best method is characterized by the one with the least number of iteration and lower CPU time. The MRMIL and MRMIL2 also have been applied in systems of linear equations for solving large scale matrix problems. Both MRMIL and MRMIL2 methods are theoretically proven to satisf, the sufficient descent and global convergence properties. From the obtained results, the MRMIL2 and MLS methods show the highest percentage of successfully solving the test problems, which are 98.39%. Meanwhile, the MPRP, MRMIL, MCD and MFR methods able to solve 97.04%,96.51%,86.02% and85.75% ofthe standard optimization problems, respectively. Both new methods converge faster and have good performance compared to the other methods. Based on the numerical results, the proposed melhods proven to converge globally thus supporting the theoretical proofs. The finding shows the MRMIL2 method is better than other CG methods. Meanwhile, MRMIL places the third after MLS and MPRP with the difference of 1.88% and 0.53% respectively. Additionally, the numerical results based on relative error also show that the MRMIL and MRMIL2 CG methods are comparable with other CG methods when they are applied in system of linear equations, that are 5.8651x 10-5 and 5.8591x 10-6, respectively. As a conclusion, the MRMIL and MRMIL2 have capabilities for solving unconstrained optimization problems and systems oflinear equations that are competitive with other CG methods. |
| title | 2020_Modified Spectral Conjugate Gradient Methods For Unconstrained Optimization and System of Linear Equations |
| title_full | 2020_Modified Spectral Conjugate Gradient Methods For Unconstrained Optimization and System of Linear Equations |
| title_fullStr | 2020_Modified Spectral Conjugate Gradient Methods For Unconstrained Optimization and System of Linear Equations |
| title_full_unstemmed | 2020_Modified Spectral Conjugate Gradient Methods For Unconstrained Optimization and System of Linear Equations |
| title_short | 2020_Modified Spectral Conjugate Gradient Methods For Unconstrained Optimization and System of Linear Equations |
| title_sort | 2020_modified spectral conjugate gradient methods for unconstrained optimization and system of linear equations |