A combination of Broyden-Fletcher-Goldfarb-Shanno (BFGS) and n-th section method for solving small-scale unconstrained optimization

In this research, a new inexact line search method known as n-th section method is used to obtain the step size in BFGS method. The n-th section method is the modification of the original bisection method. As in bisection method, this simple n-th section method divides each interval section with an even number of interval which is greater than two. This new proposed algorithm is compared with the original bisection, newton and secant method in terms of number of iteration. Numerical results is obtained based on small scale functions .This research shows that the algorithm is more efficient than using the ordinary line search methods. Besides, this proposed algorithm also possessed global convergence properties