LQP based interior prediction-correction method for nonlinear complementarity problems

Bingsheng He*, Lizhi Liao, Xiaoming Yuan

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

30 Citations (Scopus)


To solve nonlinear complementarity problems (NCP), at each iteration, the classical proximal point algorithm solves a well-conditioned sub-NCP while the Logarithmic-Quadratic Proximal (LQP) method solves a system of nonlinear equations (LQP system). This paper presents a practical LQP method-based prediction-correction method for NCP. The predictor is obtained via solving the LQP system approximately under significantly relaxed restriction, and the new iterate (the corrector) is computed directly by an explicit formula derived from the original LQP method. The implementations are very easy to be carried out. Global convergence of the method is proved under the same mild assumptions as the original LQP method. Finally, numerical results for traffic equilibrium problems are provided to verify that the method is effective for some practical problems.

Original languageEnglish
Pages (from-to)33-44
Number of pages12
JournalJournal of Computational Mathematics
Issue number1
Publication statusPublished - Jan 2006

Scopus Subject Areas

  • Computational Mathematics

User-Defined Keywords

  • Logarithmic-Quadratic proximal method
  • Nonlinear complementarity problems
  • Prediction-correction
  • Inexact criterion


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