Mathematical Programming

, Volume 58, Issue 1–3, pp 353–367

A nonsmooth version of Newton's method

  • Liqun Qi
  • Jie Sun


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 forC2-nonlinear programming is semismooth. Thus, the extended Newton's method can be used in the augmented Lagrangian method for solving nonlinear programs.

Key words

Newton's methods generalized Jacobian semismoothness 


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Copyright information

© The Mathematical Programming Society, Inc. 1993

Authors and Affiliations

  • Liqun Qi
    • 1
  • Jie Sun
    • 2
  1. 1.School of MathematicsThe University of New South WalesKensingtonAustralia
  2. 2.Department of Industrial Engineering and Management SciencesNorthwestern UniversityEvanstonUSA

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