Semi-smooth Newton methods for the Signorini problem

Kazufumi Ito; Karl Kunisch

Applications of Mathematics (2008)

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

Abstract

top
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.

How to cite

top

Ito, 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

top
  1. Bergounioux, M., Haddou, M., Hintermüller, M., Kunisch, K., 10.1137/S1052623498343131, SIAM J. Optim. 11 (2000), 495-521. (2000) MR1787272DOI10.1137/S1052623498343131
  2. Glowinski, R., Numerical Methods for Nonlinear Variational Problems, Springer New York (1984). (1984) Zbl0536.65054MR0737005
  3. Glowinski, R., Lions, J.-L., Trémolières, T., Analyse numérique des inéquations variationnelles, Vol. 1, Dunod Paris (1976), French. (1976) 
  4. Grisvard, P., Elliptic Problems in Nonsmooth Domains, Pitman Boston (1985). (1985) Zbl0695.35060MR0775683
  5. Grisvard, P., Singularities in Boundary Value Problems. Recherches en mathématiques appliqués 22, Masson Paris (1992). (1992) MR1173209
  6. Hintermüller, M., Ito, K., Kunisch, K., 10.1137/S1052623401383558, SIAM J. Optim. 13 (2003), 865-888. (2003) Zbl1080.90074MR1972219DOI10.1137/S1052623401383558
  7. Hintermüller, M., Kunisch, K., 10.1137/050637480, SIAM J. Control Optim. 45 (2006), 1198-1221. (2006) Zbl1121.49030MR2257219DOI10.1137/050637480
  8. Ito, K., Kunisch, K., 10.1051/m2an:2003021, M2AN, Math. Model. Numer. Anal. 37 (2003), 41-62. (2003) MR1972649DOI10.1051/m2an:2003021
  9. Ulbrich, M., 10.1137/S1052623400371569, SIAM J. Optim. 13 (2003), 805-841. (2003) Zbl1033.49039MR1972217DOI10.1137/S1052623400371569

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.