Comparisons between Newton and Quasi-Newton method in solving unconstrained optimization problems / Naznin Faiqa Khirul Fozi & Hanis Sofia Mohd Rodi
Newton and Quasi-Newton methods are widely used in solving unconstrained optimization problems. The solution to optimization problems are known as local optimum solutions and global minimum solutions. For Newton method, if the initial points are far from the solution points, it may fail to converge....
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2019
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my-uitm-ir.398092020-12-24T06:02:03Z Comparisons between Newton and Quasi-Newton method in solving unconstrained optimization problems / Naznin Faiqa Khirul Fozi & Hanis Sofia Mohd Rodi 2019-07 Khirul Fozi, Naznin Faiqa Mohd Rodi, Hanis Sofia Equations Mathematical statistics. Probabilities Analytical methods used in the solution of physical problems Algorithms Newton and Quasi-Newton methods are widely used in solving unconstrained optimization problems. The solution to optimization problems are known as local optimum solutions and global minimum solutions. For Newton method, if the initial points are far from the solution points, it may fail to converge. As an alternative, two Quasi-Newton methods which are Davidon-Fletcher-Powell (DFP) and Broyden- Fletcher-Goldfarb-Shanno (BFGS) methods were developed to overcome this problem. In this research, a comparison was made between Newton and Quasi-Newton method to determine the best method in solving unconstrained optimization problems. These methods were tested using six test functions with different initial points and their performance were compared based on the number of iterations, CPU time, and accuracy. This research also discussed about the convergence rate, global convergence and local convergence of the three methods. From numerical results, it has been shown that BFGS method is better compared to the other methods. 2019-07 Thesis https://ir.uitm.edu.my/id/eprint/39809/ https://ir.uitm.edu.my/id/eprint/39809/1/39809.pdf text en public degree Universiti Teknologi MARA Faculty of Computer and Mathematical Sciences Jusoh, Ibrahim |
| institution |
Universiti Teknologi MARA |
| collection |
UiTM Institutional Repository |
| language |
English |
| advisor |
Jusoh, Ibrahim |
| topic |
Equations Equations Analytical methods used in the solution of physical problems Algorithms |
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Equations Equations Analytical methods used in the solution of physical problems Algorithms Khirul Fozi, Naznin Faiqa Mohd Rodi, Hanis Sofia Comparisons between Newton and Quasi-Newton method in solving unconstrained optimization problems / Naznin Faiqa Khirul Fozi & Hanis Sofia Mohd Rodi |
| description |
Newton and Quasi-Newton methods are widely used in solving unconstrained optimization problems. The solution to optimization problems are known as local optimum solutions and global minimum solutions. For Newton method, if the initial points are far from the solution points, it may fail to converge. As an alternative, two Quasi-Newton methods which are Davidon-Fletcher-Powell (DFP) and Broyden- Fletcher-Goldfarb-Shanno (BFGS) methods were developed to overcome this problem. In this research, a comparison was made between Newton and Quasi-Newton method to determine the best method in solving unconstrained optimization problems. These methods were tested using six test functions with different initial points and their performance were compared based on the number of iterations, CPU time, and accuracy. This research also discussed about the convergence rate, global convergence and local convergence of the three methods. From numerical results, it has been shown that BFGS method is better compared to the other methods. |
| format |
Thesis |
| qualification_level |
Bachelor degree |
| author |
Khirul Fozi, Naznin Faiqa Mohd Rodi, Hanis Sofia |
| author_facet |
Khirul Fozi, Naznin Faiqa Mohd Rodi, Hanis Sofia |
| author_sort |
Khirul Fozi, Naznin Faiqa |
| title |
Comparisons between Newton and Quasi-Newton method in solving unconstrained optimization problems / Naznin Faiqa Khirul Fozi & Hanis Sofia Mohd Rodi |
| title_short |
Comparisons between Newton and Quasi-Newton method in solving unconstrained optimization problems / Naznin Faiqa Khirul Fozi & Hanis Sofia Mohd Rodi |
| title_full |
Comparisons between Newton and Quasi-Newton method in solving unconstrained optimization problems / Naznin Faiqa Khirul Fozi & Hanis Sofia Mohd Rodi |
| title_fullStr |
Comparisons between Newton and Quasi-Newton method in solving unconstrained optimization problems / Naznin Faiqa Khirul Fozi & Hanis Sofia Mohd Rodi |
| title_full_unstemmed |
Comparisons between Newton and Quasi-Newton method in solving unconstrained optimization problems / Naznin Faiqa Khirul Fozi & Hanis Sofia Mohd Rodi |
| title_sort |
comparisons between newton and quasi-newton method in solving unconstrained optimization problems / naznin faiqa khirul fozi & hanis sofia mohd rodi |
| granting_institution |
Universiti Teknologi MARA |
| granting_department |
Faculty of Computer and Mathematical Sciences |
| publishDate |
2019 |
| url |
https://ir.uitm.edu.my/id/eprint/39809/1/39809.pdf |
| _version_ |
1783734543251931136 |