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

Goetz Alefeld, Xiaojun Chen

Research output: Journal article publicationJournal articleAcademic researchpeer-review

13 Citations (Scopus)

Abstract

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
Volume77
Issue number261
DOIs
Publication statusPublished - 1 Jan 2008
Externally publishedYes

Keywords

  • 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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