Representations of quasi-Newton matrices and their use in limited memory methods

Richard H. Byrd, Jorge Nocedal*, Robert B. Schnabel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

403 Scopus citations


We derive compact representations of BFGS and symmetric rank-one matrices for optimization. These representations allow us to efficiently implement limited memory methods for large constrained optimization problems. In particular, we discuss how to compute projections of limited memory matrices onto subspaces. We also present a compact representation of the matrices generated by Broyden's update for solving systems of nonlinear equations.

Original languageEnglish (US)
Pages (from-to)129-156
Number of pages28
JournalMathematical Programming
Issue number1-3
StatePublished - Jan 1 1994


  • Quasi-Newton method
  • constrained optimization
  • large-scale optimization
  • limited memory method

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

Fingerprint Dive into the research topics of 'Representations of quasi-Newton matrices and their use in limited memory methods'. Together they form a unique fingerprint.

Cite this