@unpublished{BreitenbachBorzi2019,
  author    = {Breitenbach, Tim and Borz{\`i}, Alfio},
  title     = {On the SQH scheme to solve non-smooth PDE optimal control problems},
  series = {Numerical Functional Analysis and Optimization},
  journal   = {Numerical Functional Analysis and Optimization},
  doi       = {10.1080/01630563.2019.1599911},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-180936},
  year      = {2019},
  abstract  = {A sequential quadratic Hamiltonian (SQH) scheme for solving different classes of non-smooth and non-convex PDE optimal control problems is investigated considering seven different benchmark problems with increasing difficulty. These problems include linear and nonlinear PDEs with linear and bilinear control mechanisms, non-convex and discontinuous costs of the controls, L\(^1\) tracking terms, and the case of state constraints. The SQH method is based on the characterisation of optimality of PDE optimal control problems by the Pontryagin's maximum principle (PMP). For each problem, a theoretical discussion of the PMP optimality condition is given and results of numerical experiments are presented that demonstrate the large range of applicability of the SQH scheme.},
  language  = {en}
}
@article{BreitenbachBorzi2020,
  author    = {Breitenbach, Tim and Borz{\`i}, Alfio},
  title     = {The Pontryagin maximum principle for solving Fokker-Planck optimal control problems},
  series = {Computational Optimization and Applications},
  volume    = {76},
  journal   = {Computational Optimization and Applications},
  issn      = {0926-6003},
  doi       = {10.1007/s10589-020-00187-x},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-232665},
  pages     = {499-533},
  year      = {2020},
  abstract  = {The characterization and numerical solution of two non-smooth optimal control problems governed by a Fokker-Planck (FP) equation are investigated in the framework of the Pontryagin maximum principle (PMP). The two FP control problems are related to the problem of determining open- and closed-loop controls for a stochastic process whose probability density function is modelled by the FP equation. In both cases, existence and PMP characterisation of optimal controls are proved, and PMP-based numerical optimization schemes are implemented that solve the PMP optimality conditions to determine the controls sought. Results of experiments are presented that successfully validate the proposed computational framework and allow to compare the two control strategies.},
  language  = {en}
}