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Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models

Author

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  • Gonglin Yuan
  • Xiabin Duan
  • Wenjie Liu
  • Xiaoliang Wang
  • Zengru Cui
  • Zhou Sheng

Abstract

Two new PRP conjugate Algorithms are proposed in this paper based on two modified PRP conjugate gradient methods: the first algorithm is proposed for solving unconstrained optimization problems, and the second algorithm is proposed for solving nonlinear equations. The first method contains two aspects of information: function value and gradient value. The two methods both possess some good properties, as follows: 1)βk ≥ 0 2) the search direction has the trust region property without the use of any line search method 3) the search direction has sufficient descent property without the use of any line search method. Under some suitable conditions, we establish the global convergence of the two algorithms. We conduct numerical experiments to evaluate our algorithms. The numerical results indicate that the first algorithm is effective and competitive for solving unconstrained optimization problems and that the second algorithm is effective for solving large-scale nonlinear equations.

Suggested Citation

  • Gonglin Yuan & Xiabin Duan & Wenjie Liu & Xiaoliang Wang & Zengru Cui & Zhou Sheng, 2015. "Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models," PLOS ONE, Public Library of Science, vol. 10(10), pages 1-24, October.
    • Handle: RePEc:plo:pone00:0140071
    DOI: 10.1371/journal.pone.0140071
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    References listed on IDEAS

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    1. Ju-liang Zhang & Yong Wang, 2003. "A new trust region method for nonlinear equations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(2), pages 283-298, November.
    2. Gonglin Yuan & Zengxin Wei & Qiumei Zhao, 2014. "A modified Polak–Ribière–Polyak conjugate gradient algorithm for large-scale optimization problems," IISE Transactions, Taylor & Francis Journals, vol. 46(4), pages 397-413.
    3. Gonglin Yuan & Zengxin Wei, 2010. "Convergence analysis of a modified BFGS method on convex minimizations," Computational Optimization and Applications, Springer, vol. 47(2), pages 237-255, October.
    4. Gonglin Yuan & Xiwen Lu, 2009. "A modified PRP conjugate gradient method," Annals of Operations Research, Springer, vol. 166(1), pages 73-90, February.
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    Cited by:

    1. Tiantian Zhao & Wei Hong Yang, 2023. "A Nonlinear Conjugate Gradient Method Using Inexact First-Order Information," Journal of Optimization Theory and Applications, Springer, vol. 198(2), pages 502-530, August.

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