Solving quadratically constrained least squares using black box solvers
type: Item
instance of: scholarly article
title: Solving quadratically constrained least squares using black box solvers
zbMATH Open document ID: 0763.65043
DOI: 10.1007/BF02074882
author: Tony F. Chan
author: Julia A. Olkin
author: Donald W. Cooley
published in: BIT
publication date: 1993-01-16T00:00:00Z
review text: The paper presents algorithms for solving quadratically constrained linear least squares problems that do not necessarily require expensive dense matrix factorizations. It is shown that only calls to a ``black box'' unconstrained solver are required. The authors' approach exploits the matrix structure inherent in the unconstrained problem. A formula for estimating the Lagrange multiplier which depends on the amount the unconstrained solution violates the constraint and an estimate of the smallest generalized singular value are derived. Numerical tests comparing the different algorithms are presented.
reviewed by: J.Born
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C20
zbMATH DE Number: 93329
zbMATH Keywords: black box solvers
zbMATH Keywords: Lagrange multiplier
zbMATH Keywords: singular value
zbMATH Keywords: secular equation
zbMATH Keywords: numerical results
zbMATH Keywords: algorithms
zbMATH Keywords: least squares minimization problem
zbMATH Keywords: quadratic inequality constraint
Wikidata QID: Q57397425
MaRDI profile type: Publication
cites work: Algorithms for the regularization of ill-conditioned least squares problems
cites work: On the Stationary Values of a Second-Degree Polynomial on the Unit Sphere
cites work: Least squares with a quadratic constraint
cites work: A constrained eigenvalue problem
cites work: Smoothing by spline functions. II
full work available at URL: https://doi.org/10.1007/bf02074882
OpenAlex ID: W2057877490
description: scientific article; zbMATH DE number 93329