A regularized projection method for complementarity problems with non-lipschitzian functions

Goetz Alefeld, Xiaojun Chen

Research output: Journal article publicationJournal articleAcademic researchpeer-review

15 Citations (Scopus)


We consider complementarity problems involving functions which are not Lipschitz continuous at the origin. Such problems arise from the numerical solution for differential equations with non-Lipschitzian continuity, e.g. reaction and diffusion problems. We propose a regularized projection method to find an approximate solution with an estimation of the error for the non-Lipschitzian complementarity problems. We prove that the projection method globally and linearly converges to a solution of a regularized problem with any regularization parameter. Moreover, we give error bounds for a computed solution of the non-Lipschitzian problem. Numerical examples are presented to demonstrate the efficiency of the method and error bounds.
Original languageEnglish
Pages (from-to)379-395
Number of pages17
JournalMathematics of Computation
Issue number261
Publication statusPublished - 1 Jan 2008
Externally publishedYes


  • Complementarity problems
  • Error bounds
  • Non-Lipschitzian continuity
  • Projection
  • Regularization

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics


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