Article
MSC:
49K10,
49M15,
49N35,
65H10,
93B11,
93B52 | MR 2469587 | Zbl 1199.49064 | DOI: 10.1007/s10492-008-0036-7
Full entry |
PDF
(1.3 MB)
Feedback
PDF
(1.3 MB)
Feedback
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
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.
References:
[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. DOI 10.1137/S1052623498343131 | MR 1787272
[2] Glowinski, R.: Numerical Methods for Nonlinear Variational Problems. Springer New York (1984). MR 0737005 | Zbl 0536.65054
[3] Glowinski, R., Lions, J.-L., Trémolières, T.: Analyse numérique des inéquations variationnelles, Vol. 1. Dunod Paris (1976), French.
[4] Grisvard, P.: Elliptic Problems in Nonsmooth Domains. Pitman Boston (1985). MR 0775683 | Zbl 0695.35060
[5] Grisvard, P.: Singularities in Boundary Value Problems. Recherches en mathématiques appliqués 22. Masson Paris (1992). MR 1173209
[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. DOI 10.1137/S1052623401383558 | MR 1972219 | Zbl 1080.90074
[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. DOI 10.1137/050637480 | MR 2257219 | Zbl 1121.49030
[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. DOI 10.1051/m2an:2003021 | MR 1972649
[9] Ulbrich, M.: Semismooth Newton methods for operator equations in function spaces. SIAM J. Optim. 13 (2003), 805-841. DOI 10.1137/S1052623400371569 | MR 1972217 | Zbl 1033.49039
Search
Partner of
