A trust region method for solving generalized complementarity problems

Houyuan Jiang, Masao Fukushima, Liqun Qi, Defeng Sun

Research output: Journal article publicationJournal articleAcademic researchpeer-review

61 Citations (Scopus)


Based on a semismooth equation reformulation using Fischers function, a trust region algorithm is proposed for solving the generalized complementarity problem (GCP). The algorithm uses a generalized Jacobian of the function involved in the semismooth equation and adopts the squared natural residual of the semismooth equation as a merit function. The proposed algorithm is applicable to the nonlinear complementarity problem because the latter problem is a special case of the GCP. Global convergence and, under a nonsingularity assumption, local Q-superlinear (or quadratic) convergence of the algorithm are established. Moreover, calculation of a generalized Jacobian is discussed and numerical results are presented.
Original languageEnglish
Pages (from-to)140-157
Number of pages18
JournalSIAM Journal on Optimization
Issue number1
Publication statusPublished - 1 Jan 1998
Externally publishedYes


  • Generalized complementarity problem
  • Global and superlinear convergence
  • Nonlinear complementarity problem
  • Semismooth equation
  • Trust region method

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science


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