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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
Volume: 53
Issue: 5
Year: 2008
Pages: 455-468
Summary lang: English
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Category: math
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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
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Date available: 2010-07-20T12:33:37Z
Last updated: 2015-05-17
Stable URL: http://hdl.handle.net/10338.dmlcz/140334
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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
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