### 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 language | English (US) |
---|---|

Pages (from-to) | 473-485 |

Number of pages | 13 |

Journal | Mathematics of Computation |

Volume | 41 |

Issue number | 164 |

DOIs | |

State | Published - 1983 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Algebra and Number Theory
- Computational Mathematics
- Applied Mathematics

### Cite this

**An efficient algorithm for bifurcation problems of variational inequalities.** / Mittelmann, Hans.

Research output: Contribution to journal › Article

*Mathematics of Computation*, vol. 41, no. 164, pp. 473-485. https://doi.org/10.1090/S0025-5718-1983-0717697-7

}

TY - JOUR

T1 - An efficient algorithm for bifurcation problems of variational inequalities

AU - Mittelmann, Hans

PY - 1983

Y1 - 1983

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84966251938&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84966251938&partnerID=8YFLogxK

U2 - 10.1090/S0025-5718-1983-0717697-7

DO - 10.1090/S0025-5718-1983-0717697-7

M3 - Article

AN - SCOPUS:84966251938

VL - 41

SP - 473

EP - 485

JO - Mathematics of Computation

JF - Mathematics of Computation

SN - 0025-5718

IS - 164

ER -