TY - GEN A1 - Hintermüller, Michael A1 - Kovtunenko, Victor A1 - Kunisch, Karl T1 - Obstacle problems with cohesion: a hemivariational inequality approach and its efficient numerical solution N2 - Motivated by an obstacle problem for a membrane subject to cohesion forces, constrained minimization problems involving a non-convex and non-differentiable objective functional representing the total potential energy are considered. The associated first order optimality system leads to a hemi-variational inequality, which can also be interpreted as a special complementarity problem in function space. Besides an analytical investigation of first-order optimality, a primal-dual active set solver is introduced. It is associated to a limit case of a semi-smooth Newton method for a regularized version of the underlying problem class. For the numerical algorithms studied in this paper, global as well as local convergence properties are derived and verified numerically. KW - Obstacle problem with cohesion KW - generalized complementarity KW - problem KW - hemi-variational inequality KW - nonsmooth optimization KW - primaldual KW - active-set algorithm KW - generalized Newton method Y1 - 2010 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/681 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-6814 ER -