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A New Search Direction for Broyden’s Family Method in Solving Unconstrained Optimization Problems

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Recent Advances on Soft Computing and Data Mining (SCDM 2016)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 549))

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Abstract

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.

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Authors and Affiliations

  1. Faculty of Entrepreneurships and Business, Universiti Malaysia Kelantan, Kota Bharu, Malaysia

    Mohd Asrul Hery Ibrahim, Zailani Abdullah & Mohd Ashlyzan Razik

  2. Faculty of Science Computer and Information Technology, Universiti Malaya, Kuala Lumpur, Malaysia

    Tutut Herawan

Authors
  1. Mohd Asrul Hery Ibrahim
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  2. Zailani Abdullah
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  3. Mohd Ashlyzan Razik
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  4. Tutut Herawan
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Corresponding author

Correspondence to Mohd Asrul Hery Ibrahim .

Editor information

Editors and Affiliations

  1. Department of Information System, University of Malaya, Kuala Lumpur, Malaysia

    Tutut Herawan

  2. Universiti Tun Hussein Onn Malaysia, Batu Pahat, Malaysia

    Rozaida Ghazali

  3. Universiti Tun Hussein Onn Malaysia, Batu Pahat, Malaysia

    Nazri Mohd Nawi

  4. Universiti Tun Hussein Onn Malaysia, Batu Pahat, Malaysia

    Mustafa Mat Deris

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Ibrahim, M.A.H., Abdullah, Z., Razik, M.A., Herawan, T. (2017). A New Search Direction for Broyden’s Family Method in Solving Unconstrained Optimization Problems. In: Herawan, T., Ghazali, R., Nawi, N.M., Deris, M.M. (eds) Recent Advances on Soft Computing and Data Mining. SCDM 2016. Advances in Intelligent Systems and Computing, vol 549. Springer, Cham. https://doi.org/10.1007/978-3-319-51281-5_7

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  • DOI: https://doi.org/10.1007/978-3-319-51281-5_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-51279-2

  • Online ISBN: 978-3-319-51281-5

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