Variational methods for non-linear least-squares

M. Al-Baali*, R. Fletcher

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

35 Citations (Scopus)


We consider Newton-like line search descent methods for solving non-linear least-squares problems. The basis of our approach is to choose a method, or parameters within a method, by minimizing a variational measure which estimates the error in an inverse Hessian approximation. In one approach we consider sizing methods and choose sizing parameters in an optimal way. In another approach we consider various possibilities for hybrid Gauss-Newton/BFGS methods. We conclude that a simple Gauss-Newton/BFGS hybrid is both efficient and robust and we illustrate this by a range of comparative tests with other methods. These experiments include not only many well known test problems but also some new classes of large residual problem.

Original languageEnglish
Pages (from-to)405-421
Number of pages17
JournalJournal of the Operational Research Society
Issue number5
Publication statusPublished - May 1985


  • BFGS method
  • Gauss-Newton method
  • Hybrid method
  • Large residual problem
  • Non-linear least-squares
  • Sizing
  • Variational method

ASJC Scopus subject areas

  • Management Information Systems
  • Strategy and Management
  • Management Science and Operations Research
  • Marketing


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