A new search direction for Broyden’s family method in solving unconstrained optimization problems

• Main Authors: Mohd Asrul Hery Ibrahim, Zailani Abdullah, Mohd Ashlyzan Razik, Tutut Herawan
• Format: Conference or Workshop Item
• Published: 2016
• Online Access: http://discol.umk.edu.my/id/eprint/9201/; https://link.springer.com/book/10.1007/978-3-319-51281-5
• Institution: Universiti Malaysia Kelantan

The conjugate gradient method plays an important role in solving large scale problems and the quasi-Newton method is known as the most efficient method in solving unconstrained optimization problems. Hence, in this paper, we proposed a new hybrid method between conjugate gradient method and quasi-Newton method known as the CG-Broyden method. Then, the new hybrid method is compared with the quasi-Newton methods in terms of the number of iterations and CPU-time using Matlabin Windows 10 which has 4 GB RAM and running using an Intel ® Core ™ i5. Furthermore, the performance profile graphic is used to show the effectiveness of the new hybrid method.. 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.