Geodesic
Semi-smooth Newton methods for variational inequalities of the first kind
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 37 (2003) no. 1, pp. 41-62

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Semi-smooth Newton methods are analyzed for a class of variational inequalities in infinite dimensions. It is shown that they are equivalent to certain active set strategies. Global and local super-linear convergence are proved. To overcome the phenomenon of finite speed of propagation of discretized problems a penalty version is used as the basis for a continuation procedure to speed up convergence. The choice of the penalty parameter can be made on the basis of an L ∞ estimate for the penalized solutions. Unilateral as well as bilateral problems are considered.

DOI : 10.1051/m2an:2003021
Classification : 49J40, 65K10
Keywords: semi-smooth Newton methods, contact problems, variational inequalities, bilateral constraints, superlinear convergence 
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     author = {Ito, Kazufumi and Kunisch, Karl},
     title = {Semi-smooth {Newton} methods for variational inequalities of the first kind},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {41--62},
     publisher = {EDP-Sciences},
     volume = {37},
     number = {1},
     year = {2003},
     doi = {10.1051/m2an:2003021},
     zbl = {1027.49007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2003021/}
}
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Ito, Kazufumi; Kunisch, Karl. Semi-smooth Newton methods for variational inequalities of the first kind. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 37 (2003) no. 1, pp. 41-62. doi: 10.1051/m2an:2003021

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