A new nonsmooth equations approach to nonlinear complementarity problems

Houyuan Jiang, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

122 Citations (Scopus)

Abstract

Based on Fischer's function, a new nonsmooth equations approach is presented for solving nonlinear complementarity problems. Under some suitable assumptions, a local and Q-quadratic convergence result is established for the generalized Newton method applied to the system of nonsmooth equations, which is a reformulation of nonlinear complementarity problems. To globalize the generalized Newton method, a hybrid method combining the generalized Newton method with the steepest descent method is proposed. Global and Q-quadratic convergence is established for this hybrid method. Some numerical results are also reported.
Original languageEnglish
Pages (from-to)178-193
Number of pages16
JournalSIAM Journal on Control and Optimization
Volume35
Issue number1
DOIs
Publication statusPublished - 1 Jan 1997
Externally publishedYes

Keywords

  • Nonlinear complementarity problems
  • Nonsmooth equations
  • Semismoothness
  • Uniform P-functions

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

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