@article{NatemeyerWachsmuth2021,
  author    = {Natemeyer, Carolin and Wachsmuth, Daniel},
  title     = {A proximal gradient method for control problems with non-smooth and non-convex control cost},
  series = {Computational Optimization and Applications},
  volume    = {80},
  journal   = {Computational Optimization and Applications},
  number    = {2},
  issn      = {1573-2894},
  doi       = {10.1007/s10589-021-00308-0},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-269069},
  pages     = {639-677},
  year      = {2021},
  abstract  = {We investigate the convergence of the proximal gradient method applied to control problems with non-smooth and non-convex control cost. Here, we focus on control cost functionals that promote sparsity, which includes functionals of L\(^{p}\)-type for p\in [0,1). We prove stationarity properties of weak limit points of the method. These properties are weaker than those provided by Pontryagin's maximum principle and weaker than L-stationarity.},
  language  = {en}
}
@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}
}