Global convergence of Gauss-Newton-MBFGS method for solving the nonlinear least squares problem

F. Wang, D. Li, Liqun Qi

Research output: Journal article publicationJournal articleAcademic research


In this paper, by using a modified BFGS (MBFGS) update, we propose a structured MBFGS update for the nonlinear least squares problem. We then propose a hybrid method that combines the Gauss-Newton method with the structured MBFGS method for solv-ing the nonlinear least squares problem. We show that the hybrid method is globally and quadratically convergent for zero residual problems, and globally and superlinearly con-vergent for the nonzero residual problems. We also show that the unit step is essentially accepted. We also present some preliminary numerical results which show that the hybrid method is comparable with existing structured BFGS methods.
Original languageEnglish
Pages (from-to)1-19
Number of pages19
JournalAdvanced modeling and optimization
Issue number1
Publication statusPublished - 2010


  • Least squares problems
  • Gauss-Newton method
  • Structured MBFGS method
  • Global convergence

Cite this