Fixed Point Theory and Applications
Volume 2007 (2007), Article ID 32870, 8 pages
doi:10.1155/2007/32870
Research Article
Iterative Algorithm for Approximating Solutions of Maximal Monotone Operators in Hilbert Spaces
Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China
Received 11 October 2006; Revised 8 December 2006; Accepted 11 December 2006
Academic Editor: Nan-Jing Huang
Copyright © 2007 Yonghong Yao and Rudong Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We first introduce and analyze an algorithm of approximating solutions of maximal monotone operators in Hilbert spaces. Using this result, we consider the convex minimization problem of finding a minimizer of a proper lower-semicontinuous convex function and the variational problem of finding a solution of a variational inequality.