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Quantitative results on a Halpern-type proximal point algorithm

Author

Listed:
  • Laurenţiu Leuştean

    (University of Bucharest
    Simion Stoilow Institute of Mathematics of the Romanian Academy)

  • Pedro Pinto

    (Technische Universität Darmstadt)

Abstract

We apply proof mining methods to analyse a result of Boikanyo and Moroşanu on the strong convergence of a Halpern-type proximal point algorithm. As a consequence, we obtain quantitative versions of this result, providing uniform effective rates of asymptotic regularity and metastability.

Suggested Citation

  • Laurenţiu Leuştean & Pedro Pinto, 2021. "Quantitative results on a Halpern-type proximal point algorithm," Computational Optimization and Applications, Springer, vol. 79(1), pages 101-125, May.
    • Handle: RePEc:spr:coopap:v:79:y:2021:i:1:d:10.1007_s10589-021-00263-w
    DOI: 10.1007/s10589-021-00263-w
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    References listed on IDEAS

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    1. O. Boikanyo & G. Moroşanu, 2011. "Inexact Halpern-type proximal point algorithm," Journal of Global Optimization, Springer, vol. 51(1), pages 11-26, September.
    2. Yamin Wang & Fenghui Wang & Hong-Kun Xu, 2016. "Error Sensitivity for Strongly Convergent Modifications of the Proximal Point Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 901-916, March.
    3. Laurenţiu Leuştean & Adriana Nicolae & Andrei Sipoş, 2018. "An abstract proximal point algorithm," Journal of Global Optimization, Springer, vol. 72(3), pages 553-577, November.
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    Cited by:

    1. Andrei Sipoş, 2022. "Abstract strongly convergent variants of the proximal point algorithm," Computational Optimization and Applications, Springer, vol. 83(1), pages 349-380, September.

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