| Title:
|
Semi-smooth Newton methods for the Signorini problem (English) |
| Author:
|
Ito, Kazufumi |
| Author:
|
Kunisch, Karl |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
53 |
| Issue:
|
5 |
| Year:
|
2008 |
| Pages:
|
455-468 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Signorini problem |
| Keyword:
|
variational inequality |
| Keyword:
|
semi-smooth Newton method |
| Keyword:
|
primal-dual active set strategy |
| MSC:
|
49K10 |
| MSC:
|
49M15 |
| MSC:
|
49N35 |
| MSC:
|
65H10 |
| MSC:
|
93B11 |
| MSC:
|
93B52 |
| idZBL:
|
Zbl 1199.49064 |
| idMR:
|
MR2469587 |
| DOI:
|
10.1007/s10492-008-0036-7 |
| . |
| Date available:
|
2010-07-20T12:33:37Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140334 |
| . |
| Reference:
|
[1] Bergounioux, M., Haddou, M., Hintermüller, M., Kunisch, K.: A comparison of a Moreau-Yosida based active set strategy and interior point methods for constrained optimal control problems.SIAM J. Optim. 11 (2000), 495-521. MR 1787272, 10.1137/S1052623498343131 |
| Reference:
|
[2] Glowinski, R.: Numerical Methods for Nonlinear Variational Problems.Springer New York (1984). Zbl 0536.65054, MR 0737005 |
| Reference:
|
[3] Glowinski, R., Lions, J.-L., Trémolières, T.: Analyse numérique des inéquations variationnelles, Vol. 1.Dunod Paris (1976), French. |
| Reference:
|
[4] Grisvard, P.: Elliptic Problems in Nonsmooth Domains.Pitman Boston (1985). Zbl 0695.35060, MR 0775683 |
| Reference:
|
[5] Grisvard, P.: Singularities in Boundary Value Problems. Recherches en mathématiques appliqués 22.Masson Paris (1992). MR 1173209 |
| Reference:
|
[6] Hintermüller, M., Ito, K., Kunisch, K.: The primal-dual active set strategy as a semismooth Newton method.SIAM J. Optim. 13 (2003), 865-888. Zbl 1080.90074, MR 1972219, 10.1137/S1052623401383558 |
| Reference:
|
[7] Hintermüller, M., Kunisch, K.: Feasible and noninterior path-following in constrained minimization with low multiplier regularity.SIAM J. Control Optim. 45 (2006), 1198-1221. Zbl 1121.49030, MR 2257219, 10.1137/050637480 |
| Reference:
|
[8] Ito, K., Kunisch, K.: Semi-smooth Newton methods for variational inequalities of the first kind.M2AN, Math. Model. Numer. Anal. 37 (2003), 41-62. MR 1972649, 10.1051/m2an:2003021 |
| Reference:
|
[9] Ulbrich, M.: Semismooth Newton methods for operator equations in function spaces.SIAM J. Optim. 13 (2003), 805-841. Zbl 1033.49039, MR 1972217, 10.1137/S1052623400371569 |
| . |
