@phdthesis{Schindele2016,
  author    = {Schindele, Andreas},
  title     = {Proximal methods in medical image reconstruction and in nonsmooth optimal control of partial differential equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-136569},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2016},
  abstract  = {Proximal methods are iterative optimization techniques for functionals, J = J1 + J2, consisting of a differentiable part J2 and a possibly nondifferentiable part J1. In this thesis proximal methods for finite- and infinite-dimensional optimization problems are discussed. In finite dimensions, they solve l1- and TV-minimization problems that are effectively applied to image reconstruction in magnetic resonance imaging (MRI). Convergence of these methods in this setting is proved. The proposed proximal scheme is compared to a split proximal scheme and it achieves a better signal-to-noise ratio. In addition, an application that uses parallel imaging is presented. In infinite dimensions, these methods are discussed to solve nonsmooth linear and bilinear elliptic and parabolic optimal control problems. In particular, fast convergence of these methods is proved. Furthermore, for benchmarking purposes, truncated proximal schemes are compared to an inexact semismooth Newton method. Results of numerical experiments are presented to demonstrate the computational effectiveness of our proximal schemes that need less computation time than the semismooth Newton method in most cases. Results of numerical experiments are presented that successfully validate the theoretical estimates.},
  subject      = {Optimale Kontrolle},
  language  = {en}
}