On superlinear convergence of quasi-Newton methods for nonsmooth equations

Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

10 Citations (Scopus)

Abstract

We show that strong differentiability at solutions is not necessary for superlinear convergence of quasi-Newton methods for solving nonsmooth equations. We improve the superlinear convergence result of Ip and Kyparisis for general quasi-Newton methods as well as the Broyden method. For a special example, the Newton method is divergent but the Broyden method is superlinearly convergent.
Original languageEnglish
Pages (from-to)223-228
Number of pages6
JournalOperations Research Letters
Volume20
Issue number5
Publication statusPublished - 1 Jun 1997
Externally publishedYes

Keywords

  • Nonsmooth equations
  • Quasi-Newton methods
  • Superlinear convergence
  • The Broyden method

ASJC Scopus subject areas

  • Software
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering
  • Applied Mathematics

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