Extra-updates criterion for the limited memory BFGS algorithm for large scale nonlinear optimization

M. Al-Baali*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


This paper studies recent modifications of the limited memory BFGS (L-BFGS) method for solving large scale unconstrained optimization problems. Each modification technique attempts to improve the quality of the L-BFGS Hessian by employing (extra) updates in a certain sense. Because at some iterations these updates might be redundant or worsen the quality of this Hessian, this paper proposes an updates criterion to measure this quality. Hence, extra updates are employed only to improve the poor approximation of the L-BFGS Hessian. The presented numerical results illustrate the usefulness of this criterion and show that extra updates improve the performance of the L-BFGS method substantially.

Original languageEnglish
Pages (from-to)557-572
Number of pages16
JournalJournal of Complexity
Issue number2
Publication statusPublished - 2002


  • Large scale optimization
  • Limited memory BFGS method
  • Quasi-Newton methods

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Statistics and Probability
  • Numerical Analysis
  • General Mathematics
  • Control and Optimization
  • Applied Mathematics


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