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Abstract strongly convergent variants of the proximal point algorithm

Author

Listed:
  • Andrei Sipoş

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

Abstract

We prove an abstract form of the strong convergence of the Halpern-type and Tikhonov-type proximal point algorithms in CAT(0) spaces. In addition, we derive uniform and computable rates of metastability (in the sense of Tao) for these iterations using proof mining techniques.

Suggested Citation

  • Andrei Sipoş, 2022. "Abstract strongly convergent variants of the proximal point algorithm," Computational Optimization and Applications, Springer, vol. 83(1), pages 349-380, September.
    • Handle: RePEc:spr:coopap:v:83:y:2022:i:1:d:10.1007_s10589-022-00397-5
    DOI: 10.1007/s10589-022-00397-5
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    References listed on IDEAS

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    1. David Ariza-Ruiz & Genaro López-Acedo & Adriana Nicolae, 2015. "The Asymptotic Behavior of the Composition of Firmly Nonexpansive Mappings," Journal of Optimization Theory and Applications, Springer, vol. 167(2), pages 409-429, November.
    2. Laurenţiu Leuştean & Adriana Nicolae & Andrei Sipoş, 2018. "An abstract proximal point algorithm," Journal of Global Optimization, Springer, vol. 72(3), pages 553-577, November.
    3. 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.
    Full references (including those not matched with items on IDEAS)

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