Journal of Applied Mathematics
Volume 2012 (2012), Article ID 782960, 14 pages
Research Article

A Hybrid Gradient-Projection Algorithm for Averaged Mappings in Hilbert Spaces

College of Science, Civil Aviation University of China, Tianjin 300300, China

Received 18 April 2012; Accepted 21 June 2012

Academic Editor: Hong-Kun Xu

Copyright © 2012 Ming Tian and Min-Min Li. 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.


It is well known that the gradient-projection algorithm (GPA) is very useful in solving constrained convex minimization problems. In this paper, we combine a general iterative method with the gradient-projection algorithm to propose a hybrid gradient-projection algorithm and prove that the sequence generated by the hybrid gradient-projection algorithm converges in norm to a minimizer of constrained convex minimization problems which solves a variational inequality.