A combination of Broyden-Fletcher-Goldfarb-Shanno (BFGS) and n-th section method for solving small-scale unconstrained optimization
DOI:
https://doi.org/10.11113/mjfas.v0n0.560Keywords:
BFGS method, n-th section method, Step size, Global convergenceAbstract
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.
References
Adeleke O. J., Aderemi O. A., Omoregbe N. I. and Adekunle, R. A. 2013. Numerical comparison of line search criteria in nonlinear conjugate gradient algorithms, International Journal of Mathematics and Statistics Studies, 2, 24.
Andrei, N. 2008. An unconstrained optimization test functions collection. Advanced Modelling and Optimization, 10, 147-161. Retrieved from https://www.researchgate.net/publication/228737339_An_unconstrained_optimization_test_functions_collection.
Armijo, L. 1966. Minimization of functions having Lipshitz continuous first partial derivatives, Pacific Journal Mathematics, 16, 1-3.
Ding, Y., Lushi, E., & Li, Q. 2011. Investigation of quasi-Newton methods for unconstrained optimization. Simon Fraser University, Canada.
Dolan, E.D. & More, J.J. (2002).Benchmarking optimization software with performance profile. Mathematics Programming, 91, 201-213.
Goh, K.W., Mamat, M., Mohd, I. and Dasril, Y. (2012), A Novel of Step Size Selection Procedures for Steepest Descent Method, Applied Mathematical Sciences, 6, 2507 – 2518
Goldstein, A. A. (1965), On steepest descent, SIAM Journal Control, 3, 147-151.
Nujma Hayati (2015). The N-th section method : A Modification of Bisection Method, The 3rd International Innovation, Design And Articulation (i-Idea 2016), Malaysia
Wolfe, P. (1969). Convergence conditions for ascent method. SIAM Journal Control, 11, 226-235.
