On iterative algorithms for linear least squares problems with bound constraints
type: Item
instance of: scholarly article
title: On iterative algorithms for linear least squares problems with bound constraints
zbMATH Open document ID: 0722.65019
DOI: 10.1016/0024-3795(91)90009-L
published in: Linear Algebra and its Applications
publication date: 1991-01-01T00:00:00Z
review text: This paper has been inspired by recent developments in trust region methods for solving nonlinear optimization problems with simple bounds. Two new projected gradient methods are described for solving the constrained least-squares problem: \(Min\{\| Ax-b\|:\ell \leq x\leq u\}\). Which of the two methods is preferable is problem dependent. However, their performance on a wide class of problems is claimed to be superior to the authors' improvement (for large scale problems) of an algorithm proposed by \textit{P. Lötstedt} [BIT 24, 206-224 (1984; Zbl 0546.65041)].
Mathematics Subject Classification ID: 65F20
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C06
zbMATH DE Number: 4190991
zbMATH Keywords: trust region methods
zbMATH Keywords: nonlinear optimization problems
zbMATH Keywords: projected gradient methods
zbMATH Keywords: constrained least-squares problem
zbMATH Keywords: large scale problems
zbMATH Keywords: algorithm
author: Michel Bierlaire
author: Philippe L. Toint
author: Daniel Tuyttens
reviewed by: Sanjo Zlobec
describes a project that uses: CRAIG
describes a project that uses: LSQR
MaRDI profile type: Publication
cites work: On the Goldstein-Levitin-Polyak gradient projection method
cites work: Enlarging the region of convergence of Newton's method for constrained optimization
cites work: A direct method for sparse least squares problems with lower and upper bounds
cites work: Q3361799
cites work: On Linear Restricted and Interval Least-Squares Problems
cites work: Correction to the Paper on Global Convergence of a Class of Trust Region Algorithms for Optimization with Simple Bounds
cites work: Testing a Class of Methods for Solving Minimization Problems with Simple Bounds on the Variables
cites work: Inexact Newton Methods
cites work: Global and Asymptotic Convergence Rate Estimates for a Class of Projected Gradient Processes
cites work: Q4739659
cites work: Convex programming in Hilbert space
cites work: A Comparison Between Some Direct and Iterative Methods for Certain Large Scale Geodetic Least Squares Problems
cites work: Linear Least Squares with Bounds and Linear Constraints
cites work: Numerical Methods for Large Sparse Linear Least Squares Problems
cites work: Methods of conjugate gradients for solving linear systems
cites work: Q5545684
cites work: Solving the minimal least squares problem subject to bounds on the variables
cites work: Numerical Simulation of Time-Dependent Contact and Friction Problems in Rigid Body Mechanics
cites work: Algorithms for bound constrained quadratic programming problems
cites work: A generalized conjugate gradient algorithm for solving a class of quadratic programming problems
cites work: LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
cites work: Q3914337
cites work: Global Convergence of a a of Trust-Region Methods for Nonconvex Minimization in Hilbert Space
cites work: A Statistical Model for Positron Emission Tomography
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description: scientific article; zbMATH DE number 4190991