Improving the convergence of non-interior point algorithms for nonlinear complementarity problems

Liqun Qi, Defeng Sun

Research output: Journal article publicationJournal articleAcademic researchpeer-review

69 Citations (Scopus)

Abstract

Recently, based upon the Chen-Harker-Kanzow-Smale smoothing function and the trajectory and the neighbourhood techniques, Hotta and Yoshise proposed a noninterior point algorithm for solving the nonlinear complementarity problem. Their algorithm is globally convergent under a relatively mild condition. In this paper, we modify their algorithm and combine it with the superlinear convergence theory for nonlinear equations. We provide a globally linearly convergent result for a slightly updated version of the Hotta-Yoshise algorithm and show that a further modified Hotta-Yoshise algorithm is globally and superlinearly convergent, with a convergence Q-order 1 + t, under suitable conditions, where t ∈ (0,1) is an additional parameter.
Original languageEnglish
Pages (from-to)283-304
Number of pages22
JournalMathematics of Computation
Volume69
Issue number229
Publication statusPublished - 1 Jan 2000
Externally publishedYes

Keywords

  • Approximation
  • Noninterior point
  • Nonlinear complementarity problem
  • Superlinear convergence

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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