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Global convergence of a nonmonotone Broyden family method for nonconvex unconstrained minimization

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Abstract

In this paper, a nonmonotone Broyden family method is presented for the unconstrained optimization problems. The proposed line search technique is designed based on a nonmonotone line search proposed by Huang, Wan and Zhang (J. Comput. Appl. Math. 330: 586–604, 2018). The new line search technique can overcome the shortcoming that the nonmonotone line search proposed by Huang et. al only can be applied to conjugate gradient (CG) method, not Broyden family (including BFGS-type) method. The proposed method in this paper possesses some good properties: (i) a new nonmonotone line search technique is presented, (ii) the proposed nonmonotone line search technique can be applied not only to CG method but also to Broyden family (including BFGS-type) method, (iii) global convergence of the Broyden family method has been obtained with the proposed nonmonotone line search for nonconvex unconstrained minimization. In addition, numerical performance shows that the nonmonotone Broyden family method is more competitive versus the classical Broyden family method.

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Acknowledgements

We would like to thank the editor and the referees whose very helpful suggestions led to much improvement of this paper.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Center for Applied Mathematics of Guangxi, Guangxi University, Nanning, Guangxi, People’s Republic of China

    Gonglin Yuan

  2. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, People’s Republic of China

    Zhan Wang

  3. Railway Police College, Zhengzhou, Henan, 450000, People’s Republic of China

    Pengyuan Li

Authors
  1. Gonglin Yuan
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  2. Zhan Wang
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  3. Pengyuan Li
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Corresponding author

Correspondence to Zhan Wang.

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Communicated by Agnieszka Malinowska.

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This research was supported by the Guangxi science and technology base and talent project (Grant No. AD22080047), the Special Funds for Local Science and Technology Development Guided by the Central Government (No. ZY20198003), the High Level Innovation Teams and Excellent Scholars Program in Guangxi institutions of higher education (Grant No. [2019]52), the Guangxi Natural Science Key Fund (No. GXNSFDA198046), the National Natural Science Foundation of China (Grant No. 11661009), and the special foundation for Guangxi Ba Gui Scholars.

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Yuan, G., Wang, Z. & Li, P. Global convergence of a nonmonotone Broyden family method for nonconvex unconstrained minimization. Comp. Appl. Math. 41, 272 (2022). https://doi.org/10.1007/s40314-022-01980-6

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