NCP functions applied to Lagrangian globalization for the nonlinear complementarity problem

Liqun Qi, Y.F. Yang

Research output: Journal article publicationJournal articleAcademic researchpeer-review


Based on NCP functions, we present a Lagrangian globalization (LG) algorithm model for solving the nonlinear complementarity problem. In particular, this algorithm model does not depend on some specific NCP function. Under several theoretical assumptions on NCP functions we prove that the algorithm model is well-defined and globally convergent. Several NCP functions applicable to the LG-method are analyzed in details and shown to satisfy these assumptions. Furthermore, we identify not only the properties of NCP functions which enable them to be used in the LG method but also their properties which enable the strict complementarity condition to be removed from the convergence conditions of the LG method. Moreover, we construct a new NCP function which possesses some favourable properties.
Original languageEnglish
Pages (from-to)261-283
Number of pages23
JournalJournal of Global Optimization
Issue number2
Publication statusPublished - 2002


  • NCP function
  • Nonlinear complementarity problem
  • Lagrangian globalization
  • Strict complementarity condition
  • Global convergence

ASJC Scopus subject areas

  • Computer Science Applications
  • Management Science and Operations Research
  • Applied Mathematics
  • Control and Optimization


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