A nonsmooth version of Newton's method

Liqun Qi, Jie Sun

Research output: Journal article publicationJournal articleAcademic researchpeer-review

1120 Citations (Scopus)


Newton's method for solving a nonlinear equation of several variables is extended to a nonsmooth case by using the generalized Jacobian instead of the derivative. This extension includes the B-derivative version of Newton's method as a special case. Convergence theorems are proved under the condition of semismoothness. It is shown that the gradient function of the augmented Lagrangian for C2-nonlinear programming is semismooth. Thus, the extended Newton's method can be used in the augmented Lagrangian method for solving nonlinear programs.
Original languageEnglish
Pages (from-to)353-367
Number of pages15
JournalMathematical Programming
Issue number1-3
Publication statusPublished - 1 Jan 1993
Externally publishedYes


  • generalized Jacobian
  • Newton's methods
  • semismoothness

ASJC Scopus subject areas

  • Software
  • Mathematics(all)


Dive into the research topics of 'A nonsmooth version of Newton's method'. Together they form a unique fingerprint.

Cite this