Improved Hessian approximations for the limited memory BFGS method

Mehiddin Al-Baali*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

25 Citations (Scopus)


This paper considers simple modifications of the limited memory BFGS (L-BFGS) method for large scale optimization. It describes algorithms in which alternating ways of re-using a given set of stored difference vectors are outlined. The proposed algorithms resemble the L-BFGS method, except that the initial Hessian approximation is defined implicitly like the L-BFGS Hessian in terms of some stored vectors rather than the usual choice of a multiple of the unit matrix. Numerical experiments show that the new algorithms yield desirable improvement over the L-BFGS method.

Original languageEnglish
Pages (from-to)99-112
Number of pages14
JournalNumerical Algorithms
Issue number1
Publication statusPublished - 1999


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

ASJC Scopus subject areas

  • Applied Mathematics


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