Semi–smooth Newton methods for variational inequalities of the first kind

Kazufumi Ito; Karl Kunisch

Displaying similar documents to “Semi–smooth Newton methods for variational inequalities of the first kind”

Semi-smooth Newton methods for the Signorini problem

Kazufumi Ito, Karl Kunisch (2008)

Applications of Mathematics

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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.

Generalized Newton methods for the 2D-Signorini contact problem with friction in function space

Karl Kunisch, Georg Stadler (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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The 2D-Signorini contact problem with Tresca and Coulomb friction is discussed in infinite-dimensional Hilbert spaces. First, the problem with given friction (Tresca friction) is considered. It leads to a constraint non-differentiable minimization problem. By means of the Fenchel duality theorem this problem can be transformed into a constrained minimization involving a smooth functional. A regularization technique for the dual problem motivated by augmented lagrangians allows to apply...

A semi-smooth Newton method for solving elliptic equations with gradient constraints

Roland Griesse, Karl Kunisch (2009)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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Semi-smooth Newton methods for elliptic equations with gradient constraints are investigated. The one- and multi-dimensional cases are treated separately. Numerical examples illustrate the approach and as well as structural features of the solution.