An efficient line search for nonlinear least squares

M. Al-Baali, R. Fletcher

Research output: Contribution to journalArticle

35 Citations (Scopus)

Abstract

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 finding 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.

Original languageEnglish
Pages (from-to)359-377
Number of pages19
JournalJournal of Optimization Theory and Applications
Volume48
Issue number3
DOIs
Publication statusPublished - Mar 1986

Fingerprint

Nonlinear Least Squares
Line Search
Jacobian matrices
Interpolation
Polynomial Interpolation
Jacobian matrix
Unconstrained Optimization
Polynomials
Brackets
Termination
Objective function
Prototype
Numerical Results
Interval
Theorem
Nonlinear least squares

Keywords

  • line search
  • nonlinear least squares
  • sectioning
  • Unconstrained optimization

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics
  • Management Science and Operations Research

Cite this

An efficient line search for nonlinear least squares. / Al-Baali, M.; Fletcher, R.

In: Journal of Optimization Theory and Applications, Vol. 48, No. 3, 03.1986, p. 359-377.

Research output: Contribution to journalArticle

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