TY - GEN A1 - de los Reyes, Juan-Carlos A1 - Hintermüller, Michael T1 - A duality based semismooth Newton framework for solving variational inequalities of the second kind N2 - 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. KW - Variational inequalities of the second kind KW - semi-smooth Newton methods KW - Moreau- KW - Yosida regularization Y1 - 2010 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/680 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-6800 ER -