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Error Sensitivity for Strongly Convergent Modifications of the Proximal Point Algorithm

Author

Listed:
  • Yamin Wang

    (Henan Normal University
    Henan Normal University
    East China University of Science and Technology)

  • Fenghui Wang

    (Luoyang Normal University)

  • Hong-Kun Xu

    (Hangzhou Dianzi University
    King Abdulaziz University)

Abstract

The proximal point algorithm plays an important role in finding zeros of maximal monotone operators. It has however only weak convergence in the infinite-dimensional setting. In the present paper, we provide two contraction-proximal point algorithms. The strong convergence of the two algorithms is proved under two different accuracy criteria on the errors. A new technique of argument is used, and this makes sure that our conditions, which are sufficient for the strong convergence of the algorithms, are weaker than those used by several other authors.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:168:y:2016:i:3:d:10.1007_s10957-015-0835-4
    DOI: 10.1007/s10957-015-0835-4
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    References listed on IDEAS

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    1. Fenghui Wang, 2011. "A note on the regularized proximal point algorithm," Journal of Global Optimization, Springer, vol. 50(3), pages 531-535, July.
    2. Fenghui Wang & Huanhuan Cui, 2012. "On the contraction-proximal point algorithms with multi-parameters," Journal of Global Optimization, Springer, vol. 54(3), pages 485-491, November.
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    Cited by:

    1. Behzad Djafari Rouhani & Sirous Moradi, 2019. "Strong Convergence of Regularized New Proximal Point Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 864-882, June.
    2. Fenghui Wang, 2022. "The Split Feasibility Problem with Multiple Output Sets for Demicontractive Mappings," Journal of Optimization Theory and Applications, Springer, vol. 195(3), pages 837-853, December.
    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.

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