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. 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.