A parameterized Newton method and a quasi-Newton method for nonsmooth equations

Xiaojun Chen, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

55 Citations (Scopus)


This paper presents a parameterized Newton method using generalized Jacobians and a Broyden-like method for solving nonsmooth equations. The former ensures that the method is well-defined even when the generalized Jacobian is singular. The latter is constructed by using an approximation function which can be formed for nonsmooth equations arising from partial differential equations and nonlinear complementarity problems. The approximation function method generalizes the splitting function method for nonsmooth equations. Locally superlinear convergence results are proved for the two methods. Numerical examples are given to compare the two methods with some other methods.
Original languageEnglish
Pages (from-to)157-179
Number of pages23
JournalComputational Optimization and Applications
Issue number2
Publication statusPublished - 1 May 1994
Externally publishedYes


  • Broyden-like method
  • Newton's method
  • nonsmooth equations

ASJC Scopus subject areas

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics
  • Management Science and Operations Research


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