[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Log in

A note on the regularized proximal point algorithm

  • Published:
Journal of Global Optimization Aims and scope Submit manuscript

Abstract

Recently, Xu (J Glob Optim 36:115–125 (2006)) introduced a regularized proximal point algorithm for approximating a zero of a maximal monotone operator. In this note, we shall prove the strong convergence of this algorithm under some weaker conditions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bauschke H.H., Combettes P.L.: A weak-to-strong convergence principle for fejér-monotone methods in hilbert spaces. Math. Oper. Res. 26, 248–264 (2001)

    Article  Google Scholar 

  2. Goebel K., Kirk W.A.: Topics on Metric Fixed Point Theory. Cambridge University Press, Cambridge (1990)

    Book  Google Scholar 

  3. Güler O.: On the convergence of the proximal point algorithm for convex optimization. SIAM J. Control Optim. 29, 403–419 (1991)

    Article  Google Scholar 

  4. Lehdili N., Moudafi A.: Combining the proximal algorithm and Tikhonov method. Optimization 37, 239–252 (1996)

    Article  Google Scholar 

  5. Rockafellar R.T.: Monotone operators and the proximal point algorithm. SIAM J. Control Optim. 14, 877–898 (1976)

    Article  Google Scholar 

  6. Solodov M.V., Svaiter B.F.: Forcing strong convergence of proximal point iterations in a hilbert space. Math. Progr. Ser. A 87, 189–202 (2000)

    Google Scholar 

  7. Song Y., Yang C.: A note on a paper a regularization method for the proximal point algorithm. J. Glob. Optim. 43, 171–174 (2009)

    Article  Google Scholar 

  8. Suzuki T.: A sufficient and necessary condition for Halpern-type strong convergence to fixed points of nonexpansive mappings. Proc. Amer. Math. Soc. 135, 99–106 (2007)

    Article  Google Scholar 

  9. Xu H.K.: Iterative algorithms for nonlinear operators. J. Lond. Math. Soc. 66, 240–256 (2002)

    Article  Google Scholar 

  10. Xu H.K.: A regularization method for the proximal point algorithm. J. Glob. Optim. 36, 115–125 (2006)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Fenghui Wang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, F. A note on the regularized proximal point algorithm. J Glob Optim 50, 531–535 (2011). https://doi.org/10.1007/s10898-010-9611-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10898-010-9611-z

Keywords

Navigation