Preprint No.
A-01-02
Ralf Kornhuber
On constrained Newton linearization and multigrid
for variational inequalities
Abstract:
We consider the fast solution of a class of large,
piecewise smooth minimization problems.
For lack of smoothness, usual Newton multigrid methods cannot be
applied. We propose a new approach based on a combination of
convex minization with constrained Newton linearization.
No regularization is involved.
We show global convergence of the resulting monotone multigrid methods
and give polylogarithmic upper bounds for the asymptotic convergence
rates. Efficiency is illustrated by numerical experiments.
Keywords: nonlinear multigrid methods, variational inequalities
Mathematics Subject Classification (MSC2000): Primary 65N55, 65K10. Secondary 49M20, 49M15
Language: ENG
Available: Pr-A-01-02.ps (24MB)
Pr-A-01-02.ps.gz (1.8MB)
Contact: Ralf Kornhuber, Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (kornhube@math.fu-berlin.de)
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