OBSTACLE PROBLEMS WITH COHESION: A HEMIVARIATIONAL INEQUALITY APPROACH AND ITS EFFICIENT NUMERICAL SOLUTION*

Abstract. Motivated by an obstacle problem for a membrane subject to cohesion forces, constrained minimization problems involving a nonconvex and nondifferentiable objective functional representing the total potential energy are considered. The associated first-order optimality system leads to a hemivariational in-equality, 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 asso-ciated to a limit case of a semismooth 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. Key words. obstacle problem with cohesion, generalized complementarity problem, hemivariational inequality, nonsmooth optimization, primal-dual active set algorithm, generalized Newton metho