A regularization Newton method for solving nonlinear complementarity problems

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Abstract

In this paper we construct a regularization Newton method for solving the nonlinear complementarity problem (NCP(F)) and analyze its convergence properties under the assumption that F is a P0-function. We prove that every accumulation point of the sequence of iterates is a solution of NCP(F) and that the sequence of iterates is bounded if the solution set of NCP(F) is nonempty and bounded. Moreover, if F is a monotone and Lipschitz continuous function, we prove that the sequence of iterates is bounded if and only if the solution set of NCP(F) is nonempty by setting t = 1/2, where t ? [1/2, 1] is a parameter. If NCP(F) has alocally unique solution and satisfies a nonsingularity condition, then the convergence rate is superlinear (quadratic) without strict complementarity conditions. At each step, we only solve a linear system of equations. Numerical results are provided and further applications to other problems are discussed. © 1999 Springer-Verlag New York Inc.
Original languageEnglish
Pages (from-to)315-339
Number of pages25
JournalApplied Mathematics and Optimization
Volume40
Issue number3
DOIs
Publication statusPublished - 1 Jan 1999
Externally publishedYes

Keywords

  • Convergence
  • Generalized Newton method
  • Nonlinear complementarity problem
  • Nonsmooth equations
  • Regularization

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

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