Latest publications

• Anton Schiela, Roland Herzog and Ronny Bergmann
  Nonlinear Fenchel conjugates, 2024
  
  arXiv:2409.04492
  bibtex

  @ONLINE{SchielaHerzogBergmann:2024:1,
    AUTHOR = {Schiela, Anton and Herzog, Roland and Bergmann, Ronny},
    DATE = {2024-09},
    EPRINT = {2409.04492},
    EPRINTTYPE = {arXiv},
    TITLE = {Nonlinear Fenchel conjugates},
  }

• Ronny Bergmann, Roland Herzog and Hajg Jasa
  The Riemannian convex bundle method, 2024
  
  arXiv:2402.13670
  bibtex

  @ONLINE{BergmannHerzogJasa:2024:1,
    AUTHOR = {Bergmann, Ronny and Herzog, Roland and Jasa, Hajg},
    DATE = {2024-02},
    EPRINT = {2402.13670},
    EPRINTTYPE = {arXiv},
    TITLE = {The Riemannian convex bundle method},
  }

• Lukas Baumgärtner, Ronny Bergmann, Roland Herzog, Stephan Schmidt and José Vidal-Núñez
  Total generalized variation for piecewise constant functions on triangular meshes with applications in imaging
  SIAM Journal on Imaging Sciences 16(1), p.313-339, 2023
  
  arXiv:2206.12331 doi:10.1137/22m1505281
  bibtex

  @ARTICLE{BaumgaertnerBergmannHerzogSchmidtVidalNunez:2023:1,
    AUTHOR = {Baumgärtner, Lukas and Bergmann, Ronny and Herzog, Roland and Schmidt, Stephan and Vidal-Núñez, José},
    PUBLISHER = {Society for Industrial \& Applied Mathematics (SIAM)},
    DATE = {2023-02},
    DOI = {10.1137/22m1505281},
    EPRINT = {2206.12331},
    EPRINTTYPE = {arXiv},
    JOURNALTITLE = {SIAM Journal on Imaging Sciences},
    NUMBER = {1},
    PAGES = {313--339},
    TITLE = {Total generalized variation for piecewise constant functions on triangular meshes with applications in imaging},
    VOLUME = {16},
  }

• Ronny Bergmann, Roland Herzog, Julián Ortiz López and Anton Schiela
  First- and second-order analysis for optimization problems with manifold-valued constraints
  Journal of Optimization Theory and Applications 195(2), p.596-623, 2022
  
  arXiv:2110.04882 doi:10.1007/s10957-022-02107-x
  bibtex

  @ARTICLE{BergmannHerzogOrtizLopezSchiela:2022:1,
    AUTHOR = {Bergmann, Ronny and Herzog, Roland and Ortiz López, Julián and Schiela, Anton},
    PUBLISHER = {Springer Science and Business Media LLC},
    DATE = {2022-09},
    DOI = {10.1007/s10957-022-02107-x},
    EPRINT = {2110.04882},
    EPRINTTYPE = {arXiv},
    JOURNALTITLE = {Journal of Optimization Theory and Applications},
    NUMBER = {2},
    PAGES = {596--623},
    TITLE = {First- and second-order analysis for optimization problems with manifold-valued constraints},
    VOLUME = {195},
  }

• Maurício Silva Louzeiro, Ronny Bergmann and Roland Herzog
  Fenchel duality and a separation theorem on Hadamard manifolds
  SIAM Journal on Optimization 32(2), p.854-873, 2022
  
  arXiv:2102.11155 doi:10.1137/21m1400699
  bibtex

  @ARTICLE{SilvaLouzeiroBergmannHerzog:2022:1,
    AUTHOR = {Silva Louzeiro, Maurício and Bergmann, Ronny and Herzog, Roland},
    PUBLISHER = {Society for Industrial \& Applied Mathematics (SIAM)},
    DATE = {2022-05},
    DOI = {10.1137/21m1400699},
    EPRINT = {2102.11155},
    EPRINTTYPE = {arXiv},
    JOURNALTITLE = {SIAM Journal on Optimization},
    NUMBER = {2},
    PAGES = {854--873},
    TITLE = {Fenchel duality and a separation theorem on Hadamard manifolds},
    VOLUME = {32},
  }

• Ronny Bergmann, Roland Herzog, Maurício Silva Louzeiro, Daniel Tenbrinck and José Vidal-Núñez
  Fenchel duality theory and a primal-dual algorithm on Riemannian manifolds
  Foundations of Computational Mathematics 21(6), p.1465-1504, 2021
  
  arXiv:1908.02022 doi:10.1007/s10208-020-09486-5
  bibtex

  @ARTICLE{BergmannHerzogSilvaLouzeiroTenbrinckVidalNunez:2021:1,
    AUTHOR = {Bergmann, Ronny and Herzog, Roland and Silva Louzeiro, Maurício and Tenbrinck, Daniel and Vidal-Núñez, José},
    PUBLISHER = {Springer Science and Business Media LLC},
    DATE = {2021-01},
    DOI = {10.1007/s10208-020-09486-5},
    EPRINT = {1908.02022},
    EPRINTTYPE = {arXiv},
    JOURNALTITLE = {Foundations of Computational Mathematics},
    NUMBER = {6},
    PAGES = {1465--1504},
    TITLE = {Fenchel duality theory and a primal-dual algorithm on Riemannian manifolds},
    VOLUME = {21},
  }

• Lukas Baumgärtner, Ronny Bergmann, Roland Herzog, Stephan Schmidt, José Vidal-Núñez and Manuel Weiß
  Mesh denoising and inpainting using the total variation of the normal and a shape Newton approach, 2020
  
  arXiv:2012.11748
  bibtex

  @ONLINE{BaumgaertnerBergmannHerzogSchmidtVidalNunezWeiss:2020:1,
    AUTHOR = {Baumgärtner, Lukas and Bergmann, Ronny and Herzog, Roland and Schmidt, Stephan and Vidal-Núñez, José and Weiß, Manuel},
    DATE = {2020-12},
    EPRINT = {2012.11748},
    EPRINTTYPE = {arXiv},
    TITLE = {Mesh denoising and inpainting using the total variation of the normal and a shape Newton approach},
  }

• Ronny Bergmann, Marc Herrmann, Roland Herzog, Stephan Schmidt and José Vidal-Núñez
  Total variation of the normal vector field as shape prior
  Inverse Problems 36(5), 2020
  
  arXiv:1902.07240 doi:10.1088/1361-6420/ab6d5b
  bibtex

  @ARTICLE{BergmannHerrmannHerzogSchmidtVidalNunez:2020:1,
    AUTHOR = {Bergmann, Ronny and Herrmann, Marc and Herzog, Roland and Schmidt, Stephan and Vidal-Núñez, José},
    DATE = {2020},
    DOI = {10.1088/1361-6420/ab6d5b},
    EPRINT = {1902.07240},
    EPRINTTYPE = {arXiv},
    JOURNALTITLE = {Inverse Problems},
    NUMBER = {5},
    PAGES = {054004},
    TITLE = {Total variation of the normal vector field as shape prior},
    VOLUME = {36},
  }