GLOBAL CONVERGENCE OF A CLASS OF QUASI-NEWTON METHODS ON CONVEX PROBLEMS.

Richard H. Byrd*, Jorge Nocedal, Yuan Ya-Xiang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

200 Scopus citations

Abstract

We study the global convergence properties of the restricted Broyden class of quasi-Newton methods, when applied to a convex objective function. We assume that the line search satisfies a standard sufficient decrease condition and that the initial Hessian approximation is any positive definite matrix. We show global and superlinear convergence for this class of methods, except for DFP. The analysis gives us insight into the properties of these algorithms; in particular it shows that DFP lacks a very desirable self-correcting property possessed by BFGS.

Original languageEnglish (US)
Pages (from-to)1171-1190
Number of pages20
JournalSIAM Journal on Numerical Analysis
Volume24
Issue number5
DOIs
StatePublished - 1987

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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