@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}
}
@article{GaviraghiSchindeleAnnunziatoetal.2016,
  author    = {Gaviraghi, Beatrice and Schindele, Andreas and Annunziato, Mario and Borz{\`i}, Alfio},
  title     = {On Optimal Sparse-Control Problems Governed by Jump-Diffusion Processes},
  series = {Applied Mathematics},
  volume    = {7},
  journal   = {Applied Mathematics},
  number    = {16},
  doi       = {10.4236/am.2016.716162},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-147819},
  pages     = {1978 -- 2004},
  year      = {2016},
  abstract  = {A framework for the optimal sparse-control of the probability density function of a jump-diffusion process is presented. This framework is based on the partial integro-differential Fokker-Planck (FP) equation that governs the time evolution of the probability density function of this process. In the stochastic process and, correspondingly, in the FP model the control function enters as a time-dependent coefficient. The objectives of the control are to minimize a discrete-in-time, resp. continuous-in-time, tracking functionals and its L2- and L1-costs, where the latter is considered to promote control sparsity. An efficient proximal scheme for solving these optimal control problems is considered. Results of numerical experiments are presented to validate the theoretical results and the computational effectiveness of the proposed control framework.},
  language  = {en}
}