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A descent Dai-Liao conjugate gradient method for nonlinear equations

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Abstract

In this work, we propose an algorithm for solving system of nonlinear equations. The idea is a combination of the descent Dai-Liao method by Babaie-Kafaki and Gambari (Optim. Meth. Soft. 29(3), 583–591, 2014) and the hyperplane projection method. Using the monotonicity and Lipschitz continuity assumptions, we prove that the proposed method is globally convergent. Examples of numerical experiment show that the method is promising and efficient compared to the method proposed by Sun et al. (Journal of Inequalities and Applications 236, 1–8, 2017).

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Acknowledgements

The authors are grateful to the referees for their helpful suggestions which provide an improvement of the paper.

Funding

This study was funded by the King Mongkut’s University of Technology Thonburi through the “KMUTT 55th Anniversary Commemorative Fund.” The first author was supported by the Petchra Pra Jom Klao Doctoral Scholarship Academic for Ph.D. Program at KMUTT. This project is supported by the Theoretical and Computational Science (TaCS) Center under Computational and Applied Science for Smart Innovation (CLASSIC), Faculty of Science, KMUTT.

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Authors and Affiliations

  1. KMUTTFixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok, 10140, Thailand

    Auwal Bala Abubakar & Poom Kumam

  2. Department of Mathematical Sciences, Faculty of Physical Sciences, Bayero University Kano, Kano, Nigeria

    Auwal Bala Abubakar

  3. KMUTT-Fixed Point Theory and Applications Research Group, Theoretical and Computational Science Center (TaCs), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok, 10140, Thailand

    Poom Kumam

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  1. Auwal Bala Abubakar
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  2. Poom Kumam
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Correspondence to Poom Kumam.

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Abubakar, A.B., Kumam, P. A descent Dai-Liao conjugate gradient method for nonlinear equations. Numer Algor 81, 197–210 (2019). https://doi.org/10.1007/s11075-018-0541-z

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  • DOI: https://doi.org/10.1007/s11075-018-0541-z

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