Abstract: In this study, we present a new search direction known as the CG-Broyden method which uses the search direction of the conjugate gradient method approach in the quasi-Newton methods. The new algorithm is compared with the quasi-Newton methods in terms of the number of iterations and CPU-time. The Broydens family method is used as an updating formula for the approximation of the Hessian for both methods. Our numerical analysis provides strong evidence that our CG-Broyden method is more efficient than the ordinary Broyden method. Besides, we also prove that the new algorithm is globally convergent.
Mohd Asrul Hery Ibrahim, Zahratul Amani Zakaria, Mustafa Mamat, Ummie Khalthum Mohd Yusof and Azfi Zaidi Mohammad Sofi, 2017. A New Search Direction for Broydens Family Method with Coefficient of Conjugate Gradient in Solving Unconstrained Optimization Problems. Research Journal of Applied Sciences, 12: 31-36.