An efficient line search for nonlinear least squares
type: Item
instance of: scholarly article
title: An efficient line search for nonlinear least squares
zbMATH Open document ID: 0562.90074
DOI: 10.1007/BF00940566
published in: Journal of Optimization Theory and Applications
publication date: 1986-01-01T00:00:00Z
review text: The line search subproblem in unconstrained optimization is concerned with finding an acceptable steplength which satisfies certain standard conditions. Prototype algorithms are described which guarantee to find such a step in a finite number of operations. This is achieved by first bracketing an interval of acceptable values and then reducing this bracket uniformly by the repeated use of sectioning in a systematic way. Some new theorems about convergence and termination of the line search are presented. Use of these algorithms to solve the line search subproblem in methods for nonlinear least squares is considered. We show that substantial gains in efficiency can be made by making polynomial interpolations to the individual residual functions rather than the overall objective function. We also study modified schemes in which the Jacobian matrix is evaluated as infrequently as possible, and show that further worthwhile savings can be made. Numerical results are presented.
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 49M37
Mathematics Subject Classification ID: 65K05
zbMATH DE Number: 3896677
zbMATH Keywords: line search subproblem
zbMATH Keywords: unconstrained optimization
zbMATH Keywords: sectioning
zbMATH Keywords: nonlinear least squares
author: Mehiddin Al-Baali
author: Roger Fletcher
describes a project that uses: BRENT
MaRDI profile type: Publication
cites work: On Steepest Descent
cites work: Convergence Conditions for Ascent Methods
cites work: Q3882253
cites work: Variational Methods for Non-Linear Least-Squares
cites work: Q5657612
full work available at URL: https://doi.org/10.1007/bf00940566
OpenAlex ID: W2050786966
description: scientific article; zbMATH DE number 3896677