Comparisons between Newton and Quasi-Newton method in solving unconstrained optimization problems / Naznin Faiqa Khirul Fozi & Hanis Sofia Mohd Rodi

Khirul Fozi, Naznin Faiqa and Mohd Rodi, Hanis Sofia (2019) Comparisons between Newton and Quasi-Newton method in solving unconstrained optimization problems / Naznin Faiqa Khirul Fozi & Hanis Sofia Mohd Rodi. Degree thesis, Universiti Teknologi MARA.

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Abstract

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.

Metadata

Item Type: Thesis (Degree)
Creators:
Creators
Email
Khirul Fozi, Naznin Faiqa
2016299226
Mohd Rodi, Hanis Sofia
2016299256
Contributors:
Contribution
Name
Email / ID Num.
Thesis advisor
Jusoh, Ibrahim
UNSPECIFIED
Subjects: Q Science > QA Mathematics > Equations
Q Science > QA Mathematics > Mathematical statistics. Probabilities
Q Science > QA Mathematics > Analysis > Analytical methods used in the solution of physical problems
Q Science > QA Mathematics > Instruments and machines > Electronic Computers. Computer Science > Algorithms
Divisions: Universiti Teknologi MARA, Terengganu > Kuala Terengganu Campus > Faculty of Computer and Mathematical Sciences
Programme: Bachelor of Science (Hons) Computational Mathematics
Item ID: 39809
Uncontrolled Keywords: Newton Method ; Davidon-Fletcher-Powell ; Broyden- Fletcher-Goldfarb-Shanno
URI: https://ir.uitm.edu.my/id/eprint/39809

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