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A Nonlinear Conjugate Gradient Method Using Inexact First-Order Information

Author

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  • Tiantian Zhao

    (Fudan University)

  • Wei Hong Yang

    (Fudan University)

Abstract

Conjugate gradient methods are widely used for solving nonlinear optimization problems. In some practical problems, we can only get approximate values of the objective function and its gradient. It is necessary to consider optimization algorithms that use inexact function evaluations and inexact gradients. In this paper, we propose an inexact nonlinear conjugate gradient (INCG) method to solve such problems. Under some mild conditions, the global convergence of INCG is proved. Specifically, we establish the linear convergence of INCG when the objective function is strongly convex. Numerical results demonstrate that, compared to the state-of-the-art algorithms, INCG is an effective method.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:198:y:2023:i:2:d:10.1007_s10957-023-02243-y
    DOI: 10.1007/s10957-023-02243-y
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    References listed on IDEAS

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    1. 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.
    2. DEVOLDER, Olivier & GLINEUR, François & NESTEROV, Yurii, 2011. "First-order methods of smooth convex optimization with inexact oracle," LIDAM Discussion Papers CORE 2011002, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. XiaoLiang Dong & Deren Han & Zhifeng Dai & Lixiang Li & Jianguang Zhu, 2018. "An Accelerated Three-Term Conjugate Gradient Method with Sufficient Descent Condition and Conjugacy Condition," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 944-961, December.
    4. Can Li, 2013. "A Conjugate Gradient Type Method for the Nonnegative Constraints Optimization Problems," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-6, April.
    5. Wenyu Sun & Ya-Xiang Yuan, 2006. "Optimization Theory and Methods," Springer Optimization and Its Applications, Springer, number 978-0-387-24976-6, September.
    6. Neculai Andrei, 2020. "Nonlinear Conjugate Gradient Methods for Unconstrained Optimization," Springer Optimization and Its Applications, Springer, number 978-3-030-42950-8, September.
    7. Neculai Andrei, 2020. "General Convergence Results for Nonlinear Conjugate Gradient Methods," Springer Optimization and Its Applications, in: Nonlinear Conjugate Gradient Methods for Unconstrained Optimization, chapter 0, pages 89-123, Springer.
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