2019_Enhancing Spectral Conjugate Gradient Methods For Solving Unconstrained Optimization Problems
| Format: | General Document |
|---|
| _version_ | 1860798149900107776 |
|---|---|
| building | INTELEK Repository |
| collection | Online Access |
| collectionurl | https://intelek.unisza.edu.my/intelek/pages/search.php?search=!collection3 |
| copyright | Copyright©PWB2025 |
| country | Malaysia |
| date | 2019-07-22 |
| format | General Document |
| id | 16188 |
| institution | UniSZA |
| originalfilename | 16188_4188770bda2d2f9.pdf |
| person | Usman Abbas Yakubu |
| recordtype | oai_dc |
| resourceurl | https://intelek.unisza.edu.my/intelek/pages/view.php?ref=16188 |
| sourcemedia | Server storage Scanned document |
| spelling | 16188 https://intelek.unisza.edu.my/intelek/pages/view.php?ref=16188 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 1.5 235 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) Copyright©PWB2025 2019-07-22 Conjugate gradient methods 16188_4188770bda2d2f9.pdf Usman Abbas Yakubu 2019_Enhancing Spectral Conjugate Gradient Methods For Solving Unconstrained Optimization Problems Conjugate Gradient (CG) methods are designed to solve large-scale problems due to their less memory requirement, storage locations and computational cost. However, these methods require n-steps to attain the minimizer and has a weak global convergence, low-performance in terms of number of iterations and the Central Processing Unit (CPU) time. In order to overcome the limitations, a spectral CG methods under exact and inexact line search methods is introduced. In this research, spectral CG methods with a simple modification of the scalar parameter are suggested. CG search direction of Birgin-Martinez and prominent Newton search direction are combined together using inexact line search and standard secant condition. On the other hand, CG search directions of Wei-Yao-Liu (WYL), Polak-Ribiere-Polyak (PRP) and Hestenes-Stiefel (HS) are utilized to derive a spectral parameter without standard secant condition using exact line search. The significance of these approaches is to reduce the Central Processing Unit (CPU) time and counting number of iterations. Comprehensive computational experiments are carried out to demonstrate the outcome of the new methods when compared with other CG methods for solving unconstrained optimization problems. The comparisons are established based on number of iterations and CPU time. Each method is coded using Matlab version R2015 subroutine program and run on personal computer Intel® Core™ i5-3317U, CPU @ 1.7GHz processor, with 4GB RAM memory and Windows 10 professional operating system. For each standard test functions, four initial values are randomly selected using dimensions ranging from two variables up to one hundred thousand variables. The numerical results are analysed using the performance profile. The numerical experiments conducted using standard test functions showed that the proposed spectral CG methods performed excellently and effectively on some prominent CG methods in terms of number of iterations and CPU time. The sufficient descent conditions and global convergence properties of all the new methods are proven under certain conditions. The spectral CG methods could solve all the standard test functions of average success and its equivalent compared to Modified Birgin-Martinez spectral (MSCG) method with 88.77%, spectral Wei-Yao-Liu (SWYL) method with 77.57%, spectral Polak-Ribiere-Polyak (SPRP) method with 85.83% and spectral Hestenes-Stiefel (SHS) method with 86.26% against the other CG methods. Spectral CG methods are effective, efficient and reliable in terms of counting number of iterations and CPU time. Hence, the proposed spectral methods can be an alternative to the CG methods for solving large-scale unconstrained optimization problems. Dissertations, Academic Conjugate Gradient Algorithm Spectral Conjugate Gradient Methods Mathematical Optimization Thesis |
| spellingShingle | 2019_Enhancing Spectral Conjugate Gradient Methods For Solving Unconstrained Optimization Problems |
| state | Terengganu |
| subject | Conjugate gradient methods Dissertations, Academic |
| summary | Conjugate Gradient (CG) methods are designed to solve large-scale problems due to their less memory requirement, storage locations and computational cost. However, these methods require n-steps to attain the minimizer and has a weak global convergence, low-performance in terms of number of iterations and the Central Processing Unit (CPU) time. In order to overcome the limitations, a spectral CG methods under exact and inexact line search methods is introduced. In this research, spectral CG methods with a simple modification of the scalar parameter are suggested. CG search direction of Birgin-Martinez and prominent Newton search direction are combined together using inexact line search and standard secant condition. On the other hand, CG search directions of Wei-Yao-Liu (WYL), Polak-Ribiere-Polyak (PRP) and Hestenes-Stiefel (HS) are utilized to derive a spectral parameter without standard secant condition using exact line search. The significance of these approaches is to reduce the Central Processing Unit (CPU) time and counting number of iterations. Comprehensive computational experiments are carried out to demonstrate the outcome of the new methods when compared with other CG methods for solving unconstrained optimization problems. The comparisons are established based on number of iterations and CPU time. Each method is coded using Matlab version R2015 subroutine program and run on personal computer Intel® Core™ i5-3317U, CPU @ 1.7GHz processor, with 4GB RAM memory and Windows 10 professional operating system. For each standard test functions, four initial values are randomly selected using dimensions ranging from two variables up to one hundred thousand variables. The numerical results are analysed using the performance profile. The numerical experiments conducted using standard test functions showed that the proposed spectral CG methods performed excellently and effectively on some prominent CG methods in terms of number of iterations and CPU time. The sufficient descent conditions and global convergence properties of all the new methods are proven under certain conditions. The spectral CG methods could solve all the standard test functions of average success and its equivalent compared to Modified Birgin-Martinez spectral (MSCG) method with 88.77%, spectral Wei-Yao-Liu (SWYL) method with 77.57%, spectral Polak-Ribiere-Polyak (SPRP) method with 85.83% and spectral Hestenes-Stiefel (SHS) method with 86.26% against the other CG methods. Spectral CG methods are effective, efficient and reliable in terms of counting number of iterations and CPU time. Hence, the proposed spectral methods can be an alternative to the CG methods for solving large-scale unconstrained optimization problems. |
| title | 2019_Enhancing Spectral Conjugate Gradient Methods For Solving Unconstrained Optimization Problems |
| title_full | 2019_Enhancing Spectral Conjugate Gradient Methods For Solving Unconstrained Optimization Problems |
| title_fullStr | 2019_Enhancing Spectral Conjugate Gradient Methods For Solving Unconstrained Optimization Problems |
| title_full_unstemmed | 2019_Enhancing Spectral Conjugate Gradient Methods For Solving Unconstrained Optimization Problems |
| title_short | 2019_Enhancing Spectral Conjugate Gradient Methods For Solving Unconstrained Optimization Problems |
| title_sort | 2019_enhancing spectral conjugate gradient methods for solving unconstrained optimization problems |