An efficient algorithm for bifurcation problems of variational inequalities

Research output: Contribution to journalArticle

14 Scopus citations

Abstract

For a class of variational inequalities on a Hubert space H bifurcating solutions exist and may be characterized as critical points of a functional with respect to the intersection of the level surfaces of another functional and a closed convex subset K of H. In a recent paper [13] we have used a gradient-projection type algorithm to obtain the solutions for discretizations of the variational inequalities. A related but Newton-based method is given here. Global and asymptotically quadratic convergence is proved. Numerical results show that it may be used very efficiently in following the bifurcating branches and that it compares favorably with several other algorithms. The method is also attractive for a class of nonlinear eigenvalue problems (K = H) for which it reduces to a generalized Rayleigh-quotient iteration. So some results are included for the path following in turning-point problems.

Original languageEnglish (US)
Pages (from-to)473-485
Number of pages13
JournalMathematics of Computation
Volume41
Issue number164
DOIs
StatePublished - 1983
Externally publishedYes

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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