An iterative approach to a constrained least squares problem. (21st April 2003)

• Record Type: Journal Article
• Authors: Reich, Simeon; Xu, Hong-Kun
• Is Part Of: Abstract and applied analysis. Volume 2003:Number 8(2003)
• Page Start: 503
• Page End: 512
• Publication Date: 2003-04-21
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/S1085337503212082
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : A constrained least squares problem in a Hilbert spaceH 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 ofH, 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.