Filters

2016 - 20183

More filters

2019 - 201922020 - 20221
Reset filters

Settings

Version: publishedVersion × Subject: semismooth Newton ×

Search Results

Now showing 1 - 3 of 3
  • Thumbnail Image
    Item
    A semismooth Newton method with analytical path-following for the H1-projection onto the Gibbs simplex
    (Oxford : Oxford Univ. Press, 2018) Adam, L.; Hintermüller, M.; Surowiec, T.M.
    An efficient, function-space-based second-order method for the H1-projection onto the Gibbs simplex is presented. The method makes use of the theory of semismooth Newton methods in function spaces as well as Moreau–Yosida regularization and techniques from parametric optimization. A path-following technique is considered for the regularization parameter updates. A rigorous first- and second-order sensitivity analysis of the value function for the regularized problem is provided to justify the update scheme. The viability of the algorithm is then demonstrated for two applications found in the literature: binary image inpainting and labeled data classification. In both cases, the algorithm exhibits mesh-independent behavior.
  • Thumbnail Image
    Item
    Duality results and regularization schemes for Prandtl-Reuss perfect plasticity
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Hintermüller, Michael; Rösel, Simon
    We consider the time-discretized problem of the quasi-static evolution problem in perfect plasticity posed in a non-reflexive Banach space and we derive an equivalent version in a reflexive Banach space. A primal-dual stabilization scheme is shown to be consistent with the initial problem. As a consequence, not only stresses, but also displacement and strains are shown to converge to a solution of the original problem in a suitable topology. This scheme gives rise to a well-defined Fenchel dual problem which is a modification of the usual stress problem in perfect plasticity. The dual problem has a simpler structure and turns out to be well-suited for numerical purposes. For the corresponding subproblems an efficient algorithmic approach in the infinite-dimensional setting based on the semismooth Newton method is proposed.
  • Thumbnail Image
    Item
    A semismooth Newton method with analytical path-following for the H1-projection onto the Gibbs simplex
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Adam, Lukáš; Hintermüller, Michael; Surowiec, Thomas M.
    An efficient, function-space-based second-order method for the H1-projection onto the Gibbs-simplex is presented. The method makes use of the theory of semismooth Newton methods in function spaces as well as Moreau-Yosida regularization and techniques from parametric optimization. A path-following technique is considered for the regularization parameter updates. A rigorous first and second-order sensitivity analysis of the value function for the regularized problem is provided to justify the update scheme. The viability of the algorithm is then demonstrated for two applications found in the literature: binary image inpainting and labeled data classification. In both cases, the algorithm exhibits meshindependent behavior.