eng Ansari Education and Research Society Journal of Ultra Scientist of Physical Sciences December 2009 21 3 915 922 jusps-A 1275 article Mustafa Mamat (mus@umt.edu.my 1 Mohd Asrul Hery Bin Ibrahim (asrulthey@yahoo.com.my 1 Ismail Mohd (ismail@umt.edu.my) 1 Department of Mathematics, Faculty of Science and Technology, University Malaysia Terengganu (UMT), (Malaysia) <p style="text-align: justify;">In quasi-Newton, there are several of updated approximation formulas and one of them is Broyden-Fletcher-Goldfard-Shanno (BFGS) method. The convergence of BFGS method are depends on the search direction, d_k and step size, a_k.&nbsp;To determine step size, many recent author uses only single type of step size and proved its super linear convergence but in this paper we propose a modification and combination on two step sizes in BFGS algorithm to solve unconstrained optimization problems. The numerical results based on the number of iteration and function evaluation will be provide at the end of this paper</p> <p>&nbsp;</p> https://www.ultrascientist.org/paper/1275/ exact line search estimation for line search step size superlinearly convergence, BFGSAMI.