Damped Techniques for the Limited Memory BFGS Method for Large-Scale Optimization

Mehiddin Al-Baali, Lucio Grandinetti*, Ornella Pisacane

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


This paper is aimed to extend a certain damped technique, suitable for the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method, to the limited memory BFGS method in the case of the large-scale unconstrained optimization. It is shown that the proposed technique maintains the global convergence property on uniformly convex functions for the limited memory BFGS method. Some numerical results are described to illustrate the important role of the damped technique. Since this technique enforces safely the positive definiteness property of the BFGS update for any value of the steplength, we also consider only the first Wolfe–Powell condition on the steplength. Then, as for the backtracking framework, only one gradient evaluation is performed on each iteration. It is reported that the proposed damped methods work much better than the limited memory BFGS method in several cases.

Original languageEnglish
Pages (from-to)688-699
Number of pages12
JournalJournal of Optimization Theory and Applications
Issue number2
Publication statusPublished - May 1 2014


  • Damped technique
  • Large-scale optimization
  • Line search framework
  • The limited memory BFGS method

ASJC Scopus subject areas

  • Management Science and Operations Research
  • Control and Optimization
  • Applied Mathematics


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