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Norm descent conjugate gradient methods for solving symmetric nonlinear equations

Author

Listed:
  • Yunhai Xiao
  • Chunjie Wu
  • Soon-Yi Wu

Abstract

Nonlinear conjugate gradient method is very popular in solving large-scale unconstrained minimization problems due to its simple iterative form and lower storage requirement. In the recent years, it was successfully extended to solve higher-dimension monotone nonlinear equations. Nevertheless, the research activities on conjugate gradient method in symmetric equations are just beginning. This study aims to developing, analyzing, and validating a family of nonlinear conjugate gradient methods for symmetric equations. The proposed algorithms are based on the latest, and state-of-the-art descent conjugate gradient methods for unconstrained minimization. The series of proposed methods are derivative-free, where the Jacobian information is needless at the full iteration process. We prove that the proposed methods converge globally under some appropriate conditions. Numerical results with differentiable parameter’s values and performance comparisons with another solver CGD to demonstrate the superiority and effectiveness of the proposed algorithms are reported. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Yunhai Xiao & Chunjie Wu & Soon-Yi Wu, 2015. "Norm descent conjugate gradient methods for solving symmetric nonlinear equations," Journal of Global Optimization, Springer, vol. 62(4), pages 751-762, August.
  • Handle: RePEc:spr:jglopt:v:62:y:2015:i:4:p:751-762
    DOI: 10.1007/s10898-014-0218-7
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    References listed on IDEAS

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    1. Xiao-Min An & Dong-Hui Li & Yunhai Xiao, 2011. "Sufficient descent directions in unconstrained optimization," Computational Optimization and Applications, Springer, vol. 48(3), pages 515-532, April.
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    Cited by:

    1. Mohammed Yusuf Waziri & Jamilu Sabi’u, 2015. "A Derivative-Free Conjugate Gradient Method and Its Global Convergence for Solving Symmetric Nonlinear Equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2015, pages 1-8, September.

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