Journal of Applied Mathematics
Volume 2012 (2012), Article ID 207323, 10 pages
http://dx.doi.org/10.1155/2012/207323
Research Article

A Perturbed Projection Algorithm with Inertial Technique for Split Feasibility Problem

Yazheng Dang,1,2 Yan Gao,1 and Yanli Han1,2

1School of Management, University of Shanghai for Science and Technology, 516 Jungong Road, Shanghai 200093, China
2Department of Mathematics and Information Science, Henan Polytechnic University, Henan 454001, China

Received 25 February 2012; Revised 29 March 2012; Accepted 2 April 2012

Academic Editor: Giuseppe Marino

Copyright © 2012 Yazheng Dang et al. 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

This paper deals with the split feasibility problem that requires to find a point closest to a closed convex set in one space such that its image under a linear transformation will be closest to another closed convex set in the image space. By combining perturbed strategy with inertial technique, we construct an inertial perturbed projection algorithm for solving the split feasibility problem. Under some suitable conditions, we show the asymptotic convergence. The results improve and extend the algorithms presented in Byrne (2002) and in Zhao and Yang (2005) and the related convergence theorem.