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A modified conjugate gradient method based on the self-scaling memoryless BFGS update

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Abstract

There are many conjugate gradient methods to solving unconstrained optimization problems. Compared with the conjugate gradient method, the accelerated conjugate gradient method has better numerical effects for the unconstrained optimization problem. In this paper, we propose a modified conjugate gradient method with Wolfe line search, which generates descent direction. Under mild conditions, we prove that the proposed method is globally convergent. Numerical results indicate that the proposed method is considerable for our test functions.

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Funding

This work was supported by the National Natural Science Foundation of China (No. 11961010, 61967004), Guangxi Key Laboratory of Automatic Testing Technology and Instruments, China (No. YQ19111).

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Authors and Affiliations

  1. School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, 541004, People’s Republic of China

    Xiangli Li & Wenjuan Zhao

  2. Guangxi Key Laboratory of Automatic Testing Technology and Instruments, Guilin University of Electronic Technology, Guilin, 541004, China

    Xiangli Li

  3. Fan Gong Middle School of Binzhou City (Binzhou City Sunshine High School of Xi’an Jiaotong University), Binzhou, 713500, People’s Republic of China

    Wenjuan Zhao

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  1. Xiangli Li
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  2. Wenjuan Zhao
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Correspondence to Xiangli Li.

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Li, X., Zhao, W. A modified conjugate gradient method based on the self-scaling memoryless BFGS update. Numer Algor 90, 1017–1042 (2022). https://doi.org/10.1007/s11075-021-01220-8

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  • DOI: https://doi.org/10.1007/s11075-021-01220-8

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