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Ito, Kazufumi; Kunisch, Karl

Semi-smooth Newton methods for variational inequalities of the first kinds. (English) Zbl 1027.49007

M2AN, Math. Model. Numer. Anal. 37, No. 1, 41-62 (2003).
Summary: 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 \(L^{\infty }\) estimate for the penalized solutions. Unilateral as well as bilateral problems are considered.

Cited in 54 Documents

MSC:

49J40 Variational inequalities
65K10 Numerical optimization and variational techniques
90C53 Methods of quasi-Newton type

Keywords:

semi-smooth Newton methods; contact problems; variational inequalities; bilateral constraints; superlinear convergence
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\textit{K. Ito} and \textit{K. Kunisch}, M2AN, Math. Model. Numer. Anal. 37, No. 1, 41--62 (2003; Zbl 1027.49007)
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