IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v182y2019i3d10.1007_s10957-019-01536-5.html
   My bibliography  Save this article

A Proximal Point Algorithm Revisited and Extended

Author

Listed:
  • Gheorghe Moroşanu

    (Academy of Romanian Scientists
    Babeş-Bolyai University)

  • Adrian Petruşel

    (Academy of Romanian Scientists
    Babeş-Bolyai University)

Abstract

This note is a reaction to the recent paper by Rouhani and Moradi (J Optim Theory Appl 172:222–235, 2017), where a proximal point algorithm proposed by Boikanyo and Moroşanu (Optim Lett 7:415–420, 2013) is discussed. Noticing the inappropriate formulation of that algorithm, we propose a more general algorithm for approximating zeros of a maximal monotone operator on a Hilbert space. Besides the main result on the strong convergence of the sequences generated by this new algorithm, we discuss some particular cases, including the approximation of minimizers of convex functionals and present two examples to illustrate the applicability of the algorithm. The note clarifies and extends both the papers quoted above.

Suggested Citation

  • Gheorghe Moroşanu & Adrian Petruşel, 2019. "A Proximal Point Algorithm Revisited and Extended," Journal of Optimization Theory and Applications, Springer, vol. 182(3), pages 1120-1129, September.
    • Handle: RePEc:spr:joptap:v:182:y:2019:i:3:d:10.1007_s10957-019-01536-5
    DOI: 10.1007/s10957-019-01536-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-019-01536-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-019-01536-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Behzad Djafari Rouhani & Sirous Moradi, 2017. "Strong Convergence of Two Proximal Point Algorithms with Possible Unbounded Error Sequences," Journal of Optimization Theory and Applications, Springer, vol. 172(1), pages 222-235, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Prasit Cholamjiak & Suparat Kesornprom & Nattawut Pholasa, 2019. "Weak and Strong Convergence Theorems for the Inclusion Problem and the Fixed-Point Problem of Nonexpansive Mappings," Mathematics, MDPI, vol. 7(2), pages 1-19, February.
    2. Boikanyo, Oganeditse A., 2015. "A strongly convergent algorithm for the split common fixed point problem," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 844-853.
    3. 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.
    4. Cui, Huanhuan & Su, Menglong, 2015. "On sufficient conditions ensuring the norm convergence of an iterative sequence to zeros of accretive operators," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 67-71.
    5. 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.
    6. J. H. Wang & C. Li & J.-C. Yao, 2015. "Finite Termination of Inexact Proximal Point Algorithms in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 166(1), pages 188-212, July.
    7. Peeyada, Pronpat & Suparatulatorn, Raweerote & Cholamjiak, Watcharaporn, 2022. "An inertial Mann forward-backward splitting algorithm of variational inclusion problems and its applications," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    8. Behzad Djafari Rouhani & Vahid Mohebbi, 2020. "Strong Convergence of an Inexact Proximal Point Algorithm in a Banach Space," Journal of Optimization Theory and Applications, Springer, vol. 186(1), pages 134-147, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:182:y:2019:i:3:d:10.1007_s10957-019-01536-5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.