On the existence of solutions to equality constrained least-squares problems in infinite-dimensional Hilbert spaces.
type: Item
instance of: scholarly article
title: On the existence of solutions to equality constrained least-squares problems in infinite-dimensional Hilbert spaces.
zbMATH Open document ID: 1051.47008
DOI: 10.1016/S0096-3003(01)00170-9
author: J. Ding
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: The least-squares problems with equality constraints \[ \min\| Tx-g\| , \text{ \;subject to }\| Sx-h\| =\min_{z\in X}\| Sz-h\| , \] for bounded linear operators with closed range in Hilbert spaces \(X, Y\) are considered. The author studies the problem of existence of solutions for all \(g, h \in Y\), based on results of \textit{R.~Bouldin} [Tôhoku Math. J., II. Ser. 25, 359-363 (1973; Zbl 0269.47002)]. Some necessary and sufficient conditions are given in terms of the angle between specified subspaces.
Mathematics Subject Classification ID: 47A50
Mathematics Subject Classification ID: 65J10
zbMATH DE Number: 1861189
zbMATH Keywords: least-squares problems
zbMATH Keywords: equality constraints
zbMATH Keywords: closed range
zbMATH Keywords: existence of solutions
zbMATH Keywords: angle between subspaces
reviewed by: Teresa Regińska
MaRDI profile type: Publication
cites work: Q4061081
cites work: The product of operators with closed range
cites work: Q3999065
cites work: Q3312749
cites work: A Restricted Pseudoinverse and Its Application to Constrained Minima
cites work: Perturbation Theory for the Rank-Deficient Equality Constrained Least Squares Problem
full work available at URL: s0096-3003(01)00170-9
OpenAlex ID: W2000766516
description: scientific article; zbMATH DE number 1861189