Geodesic
A duality based semismooth Newton framework for solving variational inequalities of the second kind
Juan Carlos De los Reyes1 ; Michael Hintermüller2
1Escuela Politécnica Nacional, Quito, Ecuador
2Weierstrass-Institut, Berlin, Germany
Interfaces and free boundaries, Tome 13 (2011) no. 4, pp. 437-462

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DOI

In an appropriate function space setting, semismooth Newton methods are proposed for iteratively computing the solution of a rather general class of variational inequalities (VIs) of the second kind. The Newton scheme is based on the Fenchel dual of the original VI problem which is regularized if necessary. In the latter case, consistency of the regularization with respect to the original problem is studied. The application of the general framework to specific model problems including Bingham flows, simplified friction, or total variation regularization in mathematical imaging is described in detail. Finally, numerical experiments are presented in order to verify the theoretical results.
DOI : 10.4171/ifb/267
Classification : 00-XX
Mots-clés : Variational inequalities of the second kind; semismooth Newton methods; Moreau–Yosida regularization

Juan Carlos De los Reyes  1   ; Michael Hintermüller  2

1 Escuela Politécnica Nacional, Quito, Ecuador
2 Weierstrass-Institut, Berlin, Germany 
Juan Carlos De los Reyes; Michael Hintermüller. A duality based semismooth Newton framework for solving variational inequalities of the second kind. Interfaces and free boundaries, Tome 13 (2011) no. 4, pp. 437-462. doi: 10.4171/ifb/267
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     title = {A duality based semismooth {Newton} framework for solving variational inequalities of the second kind},
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     pages = {437--462},
     year = {2011},
     volume = {13},
     number = {4},
     doi = {10.4171/ifb/267},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/267/}
}
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