Abstract and Applied Analysis
Volume 2003 (2003), Issue 8, Pages 503-512

An iterative approach to a constrained least squares problem

Simeon Reich1 and Hong-Kun Xu2

1Department of Mathematics, The Technion - Israel Institute of Technology, Haifa 32000, Israel
2Department of Mathematics, University of Durban-Westville, Private Bag X54001, Durban 4000, South Africa

Received 3 December 2001

Copyright © 2003 Simeon Reich and Hong-Kun Xu. 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.


A constrained least squares problem in a Hilbert space H is considered. The standard Tikhonov regularization method is used. In the case where the set of the constraints is the nonempty intersection of a finite collection of closed convex subsets of H, an iterative algorithm is designed. The resulting sequence is shown to converge strongly to the unique solution of the regularized problem. The net of the solutions to the regularized problems strongly converges to the minimum norm solution of the least squares problem if its solution set is nonempty.