# Semi-smooth Newton methods for the Signorini problem

Applications of Mathematics (2008)

- Volume: 53, Issue: 5, page 455-468
- ISSN: 0862-7940

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topIto, Kazufumi, and Kunisch, Karl. "Semi-smooth Newton methods for the Signorini problem." Applications of Mathematics 53.5 (2008): 455-468. <http://eudml.org/doc/37795>.

@article{Ito2008,

abstract = {Semi-smooth Newton methods are analyzed for the Signorini problem. A proper regularization is introduced which guarantees that the semi-smooth Newton method is superlinearly convergent for each regularized problem. Utilizing a shift motivated by an augmented Lagrangian framework, to the regularization term, the solution to each regularized problem is feasible. Convergence of the regularized problems is shown and a report on numerical experiments is given.},

author = {Ito, Kazufumi, Kunisch, Karl},

journal = {Applications of Mathematics},

keywords = {Signorini problem; variational inequality; semi-smooth Newton method; primal-dual active set strategy; Signorini problem; variational inequality; semi-smooth Newton method; primal-dual active set strategy},

language = {eng},

number = {5},

pages = {455-468},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Semi-smooth Newton methods for the Signorini problem},

url = {http://eudml.org/doc/37795},

volume = {53},

year = {2008},

}

TY - JOUR

AU - Ito, Kazufumi

AU - Kunisch, Karl

TI - Semi-smooth Newton methods for the Signorini problem

JO - Applications of Mathematics

PY - 2008

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 53

IS - 5

SP - 455

EP - 468

AB - Semi-smooth Newton methods are analyzed for the Signorini problem. A proper regularization is introduced which guarantees that the semi-smooth Newton method is superlinearly convergent for each regularized problem. Utilizing a shift motivated by an augmented Lagrangian framework, to the regularization term, the solution to each regularized problem is feasible. Convergence of the regularized problems is shown and a report on numerical experiments is given.

LA - eng

KW - Signorini problem; variational inequality; semi-smooth Newton method; primal-dual active set strategy; Signorini problem; variational inequality; semi-smooth Newton method; primal-dual active set strategy

UR - http://eudml.org/doc/37795

ER -

## References

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- Hintermüller, M., Ito, K., Kunisch, K., 10.1137/S1052623401383558, SIAM J. Optim. 13 (2003), 865-888. (2003) Zbl1080.90074MR1972219DOI10.1137/S1052623401383558
- Hintermüller, M., Kunisch, K., 10.1137/050637480, SIAM J. Control Optim. 45 (2006), 1198-1221. (2006) Zbl1121.49030MR2257219DOI10.1137/050637480
- Ito, K., Kunisch, K., 10.1051/m2an:2003021, M2AN, Math. Model. Numer. Anal. 37 (2003), 41-62. (2003) MR1972649DOI10.1051/m2an:2003021
- Ulbrich, M., 10.1137/S1052623400371569, SIAM J. Optim. 13 (2003), 805-841. (2003) Zbl1033.49039MR1972217DOI10.1137/S1052623400371569

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