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Further comment on another hybrid conjugate gradient algorithm for unconstrained optimization by Andrei

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Abstract

In Dai and Wen (Numer. Algor. 69, 337–341 2015), some improvements have been presented in the proof of Theorem 2 and Theorem 4 in Andrei (Numer. Algor. 47, 143–156 2008). However, due to incorrect inequalities used, the reasoning proof of Theorem 2.1 in Dai and Wen (Numer. Algor. 69, 337–341 2015) is incorrect. Moreover, the assumption on 0 < c1 ≤ 𝜃k < 1 of Theorem 2.1 cannot be deleted in Dai and Wen (Numer. Algor. 69, 337–341 2015). In this paper, the necessary corrections are made. Finally, another version of the proof process of Theorem 3.1 in (Numer. Algor. 69, 337–341 2015) is given. Throughout, we use the same notations and equation numbers as in Dai and Wen (Numer. Algor. 69, 337–341 2015), Andrei (Numer. Algor. 47, 143–156 2008).

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Acknowledgments

We are grateful to the anonymous referees for their valuable comments and suggestions that helped to improve the manuscript.

Funding

This work is supported by the National Natural Science Foundation of China (11601012), First-Class Disciplines Foundation of Ningxia (NXYLXK2017B09), and Shaanxi Province Natural Science Fund of China (2019JM252).

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Authors and Affiliations

  1. School of Science, Xi’an University of Architecture and Technology, Xi’an, 710055, China

    Xiuyun Zheng, Jiarong Shi & Wei Yang

  2. School of Mathematics and Information, Beifang University for Nationalities, Yinchuan, 750021, China

    Xiaoliang Dong

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  1. Xiuyun Zheng
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  2. Xiaoliang Dong
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  4. Wei Yang
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Correspondence to Xiuyun Zheng.

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Zheng, X., Dong, X., Shi, J. et al. Further comment on another hybrid conjugate gradient algorithm for unconstrained optimization by Andrei. Numer Algor 84, 603–608 (2020). https://doi.org/10.1007/s11075-019-00771-1

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