@article{KarlNeitzelWachsmuth2020,
  author    = {Karl, Veronika and Neitzel, Ira and Wachsmuth, Daniel},
  title     = {A Lagrange multiplier method for semilinear elliptic state constrained optimal control problems},
  series = {Computational Optimization and Applications},
  volume    = {77},
  journal   = {Computational Optimization and Applications},
  issn      = {0926-6003},
  doi       = {10.1007/s10589-020-00223-w},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-232811},
  pages     = {7831-869},
  year      = {2020},
  abstract  = {In this paper we apply an augmented Lagrange method to a class of semilinear ellip-tic optimal control problems with pointwise state constraints. We show strong con-vergence of subsequences of the primal variables to a local solution of the original problem as well as weak convergence of the adjoint states and weak-* convergence of the multipliers associated to the state constraint. Moreover, we show existence of stationary points in arbitrary small neighborhoods of local solutions of the original problem. Additionally, various numerical results are presented.},
  language  = {en}
}