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Strongly Convergent Inertial Proximal Point Algorithm Without On-line Rule

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Abstract

We present a strongly convergent Halpern-type proximal point algorithm with double inertial effects to find a zero of a maximal monotone operator in Hilbert spaces. The strong convergence results are obtained without on-line rule of the inertial parameters and the iterates. This makes our proof arguments different from what is obtainable in the literature where on-line rule is imposed on a strongly convergent proximal point algorithm with inertial extrapolation. Numerical examples with applications to image restoration and compressed sensing show that our proposed algorithm is useful and has practical advantages over existing ones.

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Data sharing was not applicable to this article as no datasets were generated or analyzed during the current study.

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The MATLAB codes employed to run the numerical experiments are available on request.

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Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa, P.O. Box 94, Pretoria, 0204, South Africa

    Lateef O. Jolaoso

  2. School of Mathematical Sciences, University of Southampton, Southampton, S017 1BJ, UK

    Lateef O. Jolaoso

  3. School of Mathematical Sciences, Zhejiang Normal University, Jinhua, 321004, People’s Republic of China

    Yekini Shehu

  4. Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taizhong, Taiwan

    Jen-Chih Yao

  5. Academy of Romanian Scientists, 50044, Bucharest, Romania

    Jen-Chih Yao

  6. Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan

    Jen-Chih Yao

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  1. Lateef O. Jolaoso
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Correspondence to Yekini Shehu.

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Jolaoso, L.O., Shehu, Y. & Yao, JC. Strongly Convergent Inertial Proximal Point Algorithm Without On-line Rule. J Optim Theory Appl 200, 555–584 (2024). https://doi.org/10.1007/s10957-023-02355-5

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