Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 240450, 11 pages
doi:10.1155/2010/240450
Strong and weak convergence of the modified proximal point algorithms in Hilbert space
Xinkuan Chai1
, Bo Li2
and Yisheng Song1
1College of Mathematics and Information Science, Henan Normal University, XinXiang 453007, China
2School of Mathematics and Statistics, AnYang Normal University, AnYang 455000, China
Abstract
For a monotone operator T, we shall show weak convergence of Rockafellar's proximal point algorithm to some zero of T and strong convergence of the perturbed version of Rockafellar's to PZu under some relaxed conditions, where PZ is the metric projection from H onto Z=T−10. Moreover, our proof techniques are simpler than some existed results.