Newton and quasi-Newton methods for a class of nonsmooth equations and related problems

Defeng Sun, J. Han

Research output: Journal article publicationJournal articleAcademic researchpeer-review

61 Citations (Scopus)


The paper presents concrete realizations of quasi-Newton methods for solving several standard problems including complementarity problems, special variational inequality problems, and the Karush-Kuhn-Tucker (KKT) system of nonlinear programming. A new approximation idea is introduced in this paper. The Q-superlinear convergence of the Newton method and the quasi-Newton method are established under suitable assumptions, in which the existence of F'(x*) is not assumed. The new algorithms only need to solve a linear equation in each step. For complementarity problems, the QR factorization on the quasi-Newton method is discussed.
Original languageEnglish
Pages (from-to)463-480
Number of pages18
JournalSIAM Journal on Optimization
Issue number2
Publication statusPublished - 1 Jan 1997
Externally publishedYes


  • Newton method
  • Nonsmooth equations
  • Q-superlinear convergence
  • Quasi-Newton method

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science

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