A new search direction for broyden's family method with coefficient of conjugate gradient method in solving unconstrained optimization problems

Mohd Asrul, Hery Ibrahim and Zahratul Amani, Zakaria and Mustafa, Mamat and Ummie Khalthum, Mohd Yusof and Azfi Zaidi, Mohammad Sofi (2017) A new search direction for broyden's family method with coefficient of conjugate gradient method in solving unconstrained optimization problems. Research Journal of Applied Sciences, 12 (1). pp. 31-36. ISSN 1993-6079

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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 Broyden's family method is used as as 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 this the new algorithm is globally convergent.

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