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An inertial accelerated outer quadratic approximation method for split feasibility problem with application to elastic net

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Abstract

In this paper, we introduce an inertial accelerated outer quadratic approximation method for solving the split feasibility problem in Hilbert spaces. The algorithm uses projections onto closed balls approximations of the original split feasibility problem involved sets. Since the projection onto the closed ball has a closed form, the proposed method is thus convenient to implement. Moreover, it uses a self-adaptive step-size which does not need any prior information of the operator norm. Under some suitable assumptions, we establish and prove a strong convergence theorem for the proposed algorithm. Finally, we provide several numerical experiments to demonstrate the performances of our proposed method. We also give the applications of our result to elastic nets. Our method generalizes and improves many results in the literature.

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Acknowledgements

This research project is supported by Thailand Science Research and Innovation (TSRI) Basic Research Fund: Fiscal year 2023 under project number FRB670073/0164. The authors also acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. Moreover, Guash Haile Taddele would like to thank the Postdoctoral Fellowship from King Mongkut’s University of Technology Thonburi (KMUTT), Thailand.

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Authors and Affiliations

  1. Fixed Point Research Laboratory, Fixed Point Theory and Applications Research Group, 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

    Guash Haile Taddele, Poom Kumam, Songpon Sriwongsa & Mahmoud Muhammad Yahaya

  2. Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Guash Haile Taddele, Poom Kumam, Songpon Sriwongsa & Mahmoud Muhammad Yahaya

Authors
  1. Guash Haile Taddele
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  2. Poom Kumam
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  3. Songpon Sriwongsa
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  4. Mahmoud Muhammad Yahaya
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All authors contributed equally to the manuscript and read and approved the final manuscript.

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Correspondence to Poom Kumam.

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Communicated by Joerg Fliege.

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Taddele, G.H., Kumam, P., Sriwongsa, S. et al. An inertial accelerated outer quadratic approximation method for split feasibility problem with application to elastic net. Comp. Appl. Math. 43, 47 (2024). https://doi.org/10.1007/s40314-023-02559-5

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