Convergence analysis of the Levenberg-Marquardt method

Xin Long Luo*, Lizhi LIAO, Hon Wah TAM

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

26 Citations (Scopus)


The Levenberg-Marquardt method is a popular method for both optimization problems and equilibrium problems in dynamical systems. In this article, we study the convergence properties of the Levenberg-Marquardt method with the standard matrix update scheme. In our global convergence proof, we relax the condition that update matrices be bounded, and only require that their norms increase at most linearly. Furthermore, we analyze its local convergence for the uniformly convex function. In this case, the Levenberg-Marquardt method has superlinear convergence, and the initial matrix can be chosen arbitrarily for the Broyden-Fletcher-Goldfarb-Shanno (BFGS) formula.

Original languageEnglish
Pages (from-to)659-678
Number of pages20
JournalOptimization Methods and Software
Issue number4
Publication statusPublished - Aug 2007

Scopus Subject Areas

  • Software
  • Control and Optimization
  • Applied Mathematics

User-Defined Keywords

  • Levenberg-Marquardt method
  • Ordinary differential equations
  • Quasi-Newton method
  • Trust region method
  • Unconstrained optimization


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