Journal of Applied Mathematics
Volume 2012 (2012), Article ID 927530, 21 pages
http://dx.doi.org/10.1155/2012/927530
Review Article

Applications of Fixed-Point and Optimization Methods to the Multiple-Set Split Feasibility Problem

Yonghong Yao,1 Rudong Chen,1 Giuseppe Marino,2 and Yeong Cheng Liou3

1Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China
2Dipartimento di Matematica, Università della Calabria, 87036 Arcavacata di Rende, Italy
3Department of Information Management, Cheng Shiu University, Kaohsiung 833, Taiwan

Received 6 February 2012; Accepted 12 February 2012

Academic Editor: Alain Miranville

Copyright © 2012 Yonghong Yao 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

The multiple-set split feasibility problem requires finding a point closest to a family of closed convex sets in one space such that its image under a linear transformation will be closest to another family of closed convex sets in the image space. It can be a model for many inverse problems where constraints are imposed on the solutions in the domain of a linear operator as well as in the operator’s range. It generalizes the convex feasibility problem as well as the two-set split feasibility problem. In this paper, we will review and report some recent results on iterative approaches to the multiple-set split feasibility problem.