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.
Similar content being viewed by others
References
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)
Goebel K., Kirk W.A.: Topics on Metric Fixed Point Theory. Cambridge University Press, Cambridge (1990)
Güler O.: On the convergence of the proximal point algorithm for convex optimization. SIAM J. Control Optim. 29, 403–419 (1991)
Lehdili N., Moudafi A.: Combining the proximal algorithm and Tikhonov method. Optimization 37, 239–252 (1996)
Rockafellar R.T.: Monotone operators and the proximal point algorithm. SIAM J. Control Optim. 14, 877–898 (1976)
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)
Song Y., Yang C.: A note on a paper a regularization method for the proximal point algorithm. J. Glob. Optim. 43, 171–174 (2009)
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)
Xu H.K.: Iterative algorithms for nonlinear operators. J. Lond. Math. Soc. 66, 240–256 (2002)
Xu H.K.: A regularization method for the proximal point algorithm. J. Glob. Optim. 36, 115–125 (2006)
Author information
Authors and Affiliations
Corresponding author
Rights 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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10898-010-9611-z