IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v54y2012i3p485-491.html
   My bibliography  Save this article

On the contraction-proximal point algorithms with multi-parameters

Author

Listed:
  • Fenghui Wang
  • Huanhuan Cui

Abstract

In this paper we consider the contraction-proximal point algorithm: $${x_{n+1}=\alpha_nu+\lambda_nx_n+\gamma_nJ_{\beta_n}x_n,}$$ where $${J_{\beta_n}}$$ denotes the resolvent of a monotone operator A. Under the assumption that lim n α n = 0, ∑ n α n = ∞, lim inf n β n > 0, and lim inf n γ n > 0, we prove the strong convergence of the iterates as well as its inexact version. As a result we improve and recover some recent results by Boikanyo and Morosanu. Copyright Springer Science+Business Media, LLC. 2012

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:54:y:2012:i:3:p:485-491
    DOI: 10.1007/s10898-011-9772-4
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-011-9772-4
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10898-011-9772-4?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. O. Boikanyo & G. Moroşanu, 2011. "Inexact Halpern-type proximal point algorithm," Journal of Global Optimization, Springer, vol. 51(1), pages 11-26, September.
    2. Fenghui Wang, 2011. "A note on the regularized proximal point algorithm," Journal of Global Optimization, Springer, vol. 50(3), pages 531-535, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    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. 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.
    6. 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).
    7. 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.

    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. Haibin Zhang & Juan Wei & Meixia Li & Jie Zhou & Miantao Chao, 2014. "On proximal gradient method for the convex problems regularized with the group reproducing kernel norm," Journal of Global Optimization, Springer, vol. 58(1), pages 169-188, January.
    2. 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.
    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. 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.
    5. 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.
    6. Hadi Khatibzadeh & Sajad Ranjbar, 2013. "On the Strong Convergence of Halpern Type Proximal Point Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 158(2), pages 385-396, August.
    7. Hui Ouyang, 2023. "Weak and strong convergence of generalized proximal point algorithms with relaxed parameters," Journal of Global Optimization, Springer, vol. 85(4), pages 969-1002, April.

    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:jglopt:v:54:y:2012:i:3:p:485-491. 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.