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Relaxed-inertial derivative-free algorithm for systems of nonlinear pseudo-monotone equations

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Abstract

Solving systems of nonlinear equations has evolved into an active research field, with numerous iterative methods being proposed. Notably, iterative methods characterized by fast convergence remain of interest. In this paper, based on the modified line search scheme by Ou and Li, we introduce a derivative-free algorithm with a relaxed-inertial technique for approximating solutions of nonlinear systems involving pseudo-monotone mappings in Euclidean space. The global convergence of the proposed algorithm is established without Lipschitz continuity of the underlying mapping. Moreover, our approach allows flexibility in selecting the inertial extrapolation step length within the interval [0, 1]. To show the efficiency of the proposed method, we embed a derivative-free search direction into the scheme. Numerical experiments are given to illustrate the efficiency of the proposed algorithm for large-scale systems and sparse signal reconstruction.

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Acknowledgements

The authors are very much indebted and grateful to the editors and anonymous referees for their valuable comments and suggestions which improved the quality of this paper.

Funding

This research was supported by the Postdoctoral Fellowship program at King Mongkut’s University of Technology Thonburi. Poom Kumam would like to acknowledge the financial support received from two sources: (i) the Centre of Excellence in Theoretical and Computational Science (TaCS-CoE) at KMUTT, and (ii) the “Mid-Career Research Grant” (Grant No. N41A640089). Additionally, this research received support from the Science Fund of the Republic of Serbia under Grant No. 7359, for the project titled “LASCADO.”

Author information

Authors and Affiliations

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

    Abdulkarim Hassan Ibrahim & Poom Kumam

  2. Interdisciplinary Research Center for Smart Mobility and Logistics, King Fahd University of Petroleum and Minerals, 31261, Dhahran, Saudi Arabia

    Abdulkarim Hassan Ibrahim

  3. University of Novi Sad, Faculty of Sciences, Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 4, 21000, Novi Sad, Serbia

    Sanja Rapajić

  4. Department of Mathematics, University of Science and Technology of Mazandaran, P.O. Box 48518-78195, Behshahr, Iran

    Ahmad Kamandi

  5. Hungarian Language Teacher Training Faculty, Subotica, University of Novi Sad, Štrosmajerova 11, 24000, Subotica, Serbia

    Zoltan Papp

  6. Subotica Tech-College of Applied Sciences, Marka Oreškovića 16, Subotica, 24000, Serbia

    Zoltan Papp

Authors
  1. Abdulkarim Hassan Ibrahim
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  2. Sanja Rapajić
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  4. Poom Kumam
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  5. Zoltan Papp
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Correspondence to Poom Kumam.

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Ibrahim, A.H., Rapajić, S., Kamandi, A. et al. Relaxed-inertial derivative-free algorithm for systems of nonlinear pseudo-monotone equations. Comp. Appl. Math. 43, 239 (2024). https://doi.org/10.1007/s40314-024-02673-y

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  • DOI: https://doi.org/10.1007/s40314-024-02673-y

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