@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}
}
@article{RoyBorziHabbal2017,
  author    = {Roy, S. and Borz{\`i}, A. and Habbal, A.},
  title     = {Pedestrian motion modelled by Fokker-Planck Nash games},
  series = {Royal Society Open Science},
  volume    = {4},
  journal   = {Royal Society Open Science},
  number    = {9},
  doi       = {10.1098/rsos.170648},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-170395},
  pages     = {170648},
  year      = {2017},
  abstract  = {A new approach to modelling pedestrians' avoidance dynamics based on a Fokker-Planck (FP) Nash game framework is presented. In this framework, two interacting pedestrians are considered, whose motion variability is modelled through the corresponding probability density functions (PDFs) governed by FP equations. Based on these equations, a Nash differential game is formulated where the game strategies represent controls aiming at avoidance by minimizing appropriate collision cost functionals. The existence of Nash equilibria solutions is proved and characterized as a solution to an optimal control problem that is solved numerically. Results of numerical experiments are presented that successfully compare the computed Nash equilibria to the output of real experiments (conducted with humans) for four test cases.},
  language  = {en}
}
@article{SchindeleBorzi2016,
  author    = {Schindele, Andreas and Borz{\`i}, Alfio},
  title     = {Proximal Methods for Elliptic Optimal Control Problems with Sparsity Cost Functional},
  series = {Applied Mathematics},
  volume    = {7},
  journal   = {Applied Mathematics},
  number    = {9},
  doi       = {10.4236/am.2016.79086},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-145850},
  pages     = {967-992},
  year      = {2016},
  abstract  = {First-order proximal methods that solve linear and bilinear elliptic optimal control problems with a sparsity cost functional are discussed. In particular, fast convergence of these methods is proved. For benchmarking purposes, inexact proximal schemes are compared to an inexact semismooth Newton method. Results of numerical experiments are presented to demonstrate the computational effectiveness of proximal schemes applied to infinite-dimensional elliptic optimal control problems and to validate the theoretical estimates.},
  language  = {en}
}