Analysis of the bfgs method with errors

Yuchen Xie, Richard Byrd, Jorge Nocedal

Research output: Contribution to journalArticlepeer-review


The classical convergence analysis of quasi-Newton methods assumes that the func- tion and gradients employed at each iteration are exact. In this paper, we consider the case when there are (bounded) errors in both computations and establish conditions under which a slight mod- ification of the BFGS algorithm with an Armijo-Wolfe line search converges to a neighborhood of the solution that is determined by the size of the errors. One of our results is an extension of the analysis presented in [4], which establishes that, for strongly convex functions, a fraction of the BFGS iterates are good iterates. We present numerical results illustrating the performance of the new BFGS method in the presence of noise.

Original languageEnglish (US)
JournalUnknown Journal
StatePublished - Jan 25 2019

ASJC Scopus subject areas

  • General

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