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A new inertial-based method for solving pseudomonotone operator equations with application

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Abstract

Many efforts have been made to develop efficient algorithms for solving system of nonlinear equations due to their applications in different branches of science. Some of the classical techniques such as Newton and quasi-Newton methods involve computing Jacobian matrix or an approximation to it at every iteration, which affects their adequacy to handle large scale problems. Recently, derivative-free algorithms have been developed to solve this system. To establish global convergence, most of these algorithms assumed the operator under consideration to be monotone. In this work, instead of been monotone, our operator under consideration is considered to be pseudomonotone which is more general than the usual monotonicity assumption in most of the existing literature. The proposed method is derivative-free, and also, an inertial step is incorporated to accelerate its speed of convergence. The global convergence of the proposed algorithm is proved under the assumptions that the underlying mapping is Lipschitz continuous and pseudomonotone. Numerical experiments on some test problems are presented to depict the advantages of the proposed algorithm in comparison with some existing ones. Finally, an application of the proposed algorithm is shown in motion control involving a 3-degrees of freedom (DOF) planar robot arm manipulator.

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Acknowledgements

The authors acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT and Center under Computational and Applied Science for Smart Innovation research Cluster (CLASSIC), Faculty of Science, KMUTT. Moreover, this research project is supported by Thailand Science Research and Innovation (TSRI) Basic Research Fund: Fiscal year 2021 under Project number 64A306000005.

Funding

This research is funded by Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT and Center under Computational and Applied Science for Smart Innovation research Cluster (CLASSIC), faculty of Science, KMUTT. The first author was supported by the Petchra Pra Jom Klao Ph.D. research Scholarship from King Mongkut’s University of Technology Thonburi (KMUTT) Thailand (Grant no. 19/2562).

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Authors and Affiliations

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

    Sani Aji & Mahmoud Muhammad Yahaya

  2. Center of Excellence in Theoretical and Computational Science (TaCS-CoE) and KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Poom Kumam & Aliyu Muhammed Awwal

  3. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan

    Poom Kumam

  4. Department of Mathematics, Faculty of Science, Gombe State University, Gombe, 760214, Nigeria

    Sani Aji, Aliyu Muhammed Awwal & Abubakar Muhammad Bakoji

  5. Faculty of Natural Sciences II, Institute of Mathematics, Martin Luther University Halle-Wittenberg, 06099, Halle (Saale), Germany

    Abubakar Muhammad Bakoji

Authors
  1. Sani Aji
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  2. Poom Kumam
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  3. Aliyu Muhammed Awwal
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  4. Mahmoud Muhammad Yahaya
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  5. Abubakar Muhammad Bakoji
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Contributions

All authors contributed equally to the manuscript and read and approved the final manuscript.

Corresponding author

Correspondence to Poom Kumam.

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Communicated by Andreas Fischer.

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Aji, S., Kumam, P., Awwal, A.M. et al. A new inertial-based method for solving pseudomonotone operator equations with application. Comp. Appl. Math. 42, 1 (2023). https://doi.org/10.1007/s40314-022-02135-3

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  • DOI: https://doi.org/10.1007/s40314-022-02135-3

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