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A New Hybrid Descent Algorithm for Large-Scale Nonconvex Optimization and Application to Some Image Restoration Problems

Author

Listed:
  • Shuai Wang

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

  • Xiaoliang Wang

    (Department of Mathematics and Science, School of Science, Zhejiang Sci-Tech University, Hangzhou 310018, China)

  • Yuzhu Tian

    (School of Mathematics, Liaoning Normal University, Dalian 116026, China)

  • Liping Pang

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

Abstract

Conjugate gradient methods are widely used and attractive for large-scale unconstrained smooth optimization problems, with simple computation, low memory requirements, and interesting theoretical information on the features of curvature. Based on the strongly convergent property of the Dai–Yuan method and attractive numerical performance of the Hestenes–Stiefel method, a new hybrid descent conjugate gradient method is proposed in this paper. The proposed method satisfies the sufficient descent property independent of the accuracy of the line search strategies. Under the standard conditions, the trust region property and the global convergence are established, respectively. Numerical results of 61 problems with 9 large-scale dimensions and 46 ill-conditioned matrix problems reveal that the proposed method is more effective, robust, and reliable than the other methods. Additionally, the hybrid method also demonstrates reliable results for some image restoration problems.

Suggested Citation

  • Shuai Wang & Xiaoliang Wang & Yuzhu Tian & Liping Pang, 2024. "A New Hybrid Descent Algorithm for Large-Scale Nonconvex Optimization and Application to Some Image Restoration Problems," Mathematics, MDPI, vol. 12(19), pages 1-16, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:19:p:3088-:d:1491128
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    References listed on IDEAS

    as
    1. Gonglin Yuan & Zengxin Wei & Zhongxing Wang, 2013. "Gradient trust region algorithm with limited memory BFGS update for nonsmooth convex minimization," Computational Optimization and Applications, Springer, vol. 54(1), pages 45-64, January.
    2. Y.H. Dai & Y. Yuan, 2001. "An Efficient Hybrid Conjugate Gradient Method for Unconstrained Optimization," Annals of Operations Research, Springer, vol. 103(1), pages 33-47, March.
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