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PRP-like algorithm for monotone operator equations

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Abstract

Many studies have been devoted to develop and improve the iterative methods for solving convex constraint nonlinear equations problem (CCP). Based on the projection technique, we introduce a derivative-free method for approximating the solution of CCP. The proposed method is suitable for solving large-scale nonlinear equations due to its lower storage requirements. The directions generated by the proposed method at every iteration are bounded. Under some mild conditions, we establish the global convergence result of the proposed method. Numerical experiments are provided to show the efficiency of the method in solving CCP. Moreover, we tested the capability of the method in solving the monotone nonlinear operator equation equivalent to the \(\ell _1\)-norm regularized minimization problem.

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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. Also, the (first) author, (Dr. Auwal Bala Abubakar) would like to thank the Postdoctoral Fellowship from King Mongkut’s University of Technology Thonburi (KMUTT), Thailand. Moreover, this research project is supported by Thailand Science Research and Innovation (TSRI) Basic Research Fund: Fiscal year 2021 under project number 64A306000005. The first author acknowledge with thanks, the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University.

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Authors and Affiliations

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

    Auwal Bala Abubakar & Poom Kumam

  2. Department of Mathematical Sciences, Bayero University, Kano, 700241, Nigeria

    Auwal Bala Abubakar & Hassan Mohammad

  3. Numerical Optimization Research Group, Bayero University, Kano, 700241, Nigeria

    Hassan Mohammad

  4. Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa, Ga-Rankuwa, 0204, Pretoria, South Africa

    Auwal Bala Abubakar

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

    Poom Kumam

  6. 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 & Abdulkarim Hassan Ibrahim

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  1. Auwal Bala Abubakar
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  2. Poom Kumam
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  3. Hassan Mohammad
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  4. Abdulkarim Hassan Ibrahim
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Correspondence to Poom Kumam.

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Abubakar, A.B., Kumam, P., Mohammad, H. et al. PRP-like algorithm for monotone operator equations. Japan J. Indust. Appl. Math. 38, 805–822 (2021). https://doi.org/10.1007/s13160-021-00462-2

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  • DOI: https://doi.org/10.1007/s13160-021-00462-2

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