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A New Hybrid Three-Term Conjugate Gradient Algorithm for Large-Scale Unconstrained Problems

Author

Listed:
  • Qi Tian

    (School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China)

  • Xiaoliang Wang

    (School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China)

  • Liping Pang

    (School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China)

  • Mingkun Zhang

    (School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China)

  • Fanyun Meng

    (School of Information and Control Engineering, Qingdao University of Technology, Qingdao 266520, China)

Abstract

Three-term conjugate gradient methods have attracted much attention for large-scale unconstrained problems in recent years, since they have attractive practical factors such as simple computation, low memory requirement, better descent property and strong global convergence property. In this paper, a hybrid three-term conjugate gradient algorithm is proposed and it owns a sufficient descent property, independent of any line search technique. Under some mild conditions, the proposed method is globally convergent for uniformly convex objective functions. Meanwhile, by using the modified secant equation, the proposed method is also global convergence without convexity assumption on the objective function. Numerical results also indicate that the proposed algorithm is more efficient and reliable than the other methods for the testing problems.

Suggested Citation

  • Qi Tian & Xiaoliang Wang & Liping Pang & Mingkun Zhang & Fanyun Meng, 2021. "A New Hybrid Three-Term Conjugate Gradient Algorithm for Large-Scale Unconstrained Problems," Mathematics, MDPI, vol. 9(12), pages 1-13, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1353-:d:573241
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    References listed on IDEAS

    as
    1. Gonglin Yuan & Zehong Meng & Yong Li, 2016. "A Modified Hestenes and Stiefel Conjugate Gradient Algorithm for Large-Scale Nonsmooth Minimizations and Nonlinear Equations," Journal of Optimization Theory and Applications, Springer, vol. 168(1), pages 129-152, January.
    2. Kaori Sugiki & Yasushi Narushima & Hiroshi Yabe, 2012. "Globally Convergent Three-Term Conjugate Gradient Methods that Use Secant Conditions and Generate Descent Search Directions for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 153(3), pages 733-757, June.
    3. Yingjie Zhou & Yulun Wu & Xiangrong Li, 2020. "A New Hybrid PRPFR Conjugate Gradient Method for Solving Nonlinear Monotone Equations and Image Restoration Problems," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-13, September.
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    5. Haishan Feng & Tingting Li, 2020. "An Accelerated Conjugate Gradient Algorithm for Solving Nonlinear Monotone Equations and Image Restoration Problems," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-12, October.
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