PD Dr. Ronny Bergmann
Member of the Research Group Numerical Mathematics (Partial Differential Equations)
+49 371 531 36098
+49 371 531 836098
Reichenhainer Str. 41, Office 609 (C47.609)
Anne-Kristin Glanzberg, Office 607, Phone +49 371 531 22500
TU Chemnitz, Faculty of Mathematics, 09107 Chemnitz, Germany
any time when present
- since 04/2018
- member of research group Numerical Mathematics (Partial Differential Equations) of Prof. Dr. R. Herzog
- Habilitation in Mathematics at the Technischen Universität Kaiserslautern , habilitation thesis: “Variational Methods in Manifold-valued Image Processing”
- 09/2013 — 03/2018
- PostDoc in the workgroup Image Processing and data analysis led by Prof. Dr. Gabriele Steidl at the Technischen Universität Kaiserslautern
- PhD at the Institute of Mathematics, Universität zu Lübeck, advisor Prof. Dr. Jürgen Prestin.
- 10/2009 — 08/2013
- Teaching Assistant, PhD student at the Institute of Mathematics, Universität zu Lübeck.
- master's degree in computer science, Institut für Mathematik, Universität zu Lübeck.
- 10/2004 — 09/2009
- studies of computer science at Universität zu Lübeck
- Bergmann, R. and Gousenbourger, P.-Y. (2018).
A variational model for data fitting on manifolds by minimizing the acceleration of a Bézier curve
Preprint, arXiv:1807.10090.We derive a variational model to fit a composite Bézier curve to a set data points on a Riemannian manifold. The resulting curve is obtained in such a way that its mean squared acceleration is minimal in addition to remaining close the data points. We approximate the acceleration by discretizing the squared second order derivative along the curve. We derive a closed-form, numerically stable and efficient algorithm to compute the gradient of a Bézier curve on manifolds with respect to its control points, expressed as a concatenation of so-called adjoint Jacobi fields. Several examples illustrate the capabilites and validity of this approach both for interpolation and approximation. The examples also illustrate that the approach outperforms previous works tackling this problem.
- Bergmann, R. and Herzog, R. (2018).
Intrinsic formulation of KKT conditions and constraint qualifications on smooth manifolds.
Preprint, arXiv:1804.06214.Karush-Kuhn-Tucker (KKT) conditions for equality and inequality constrained optimization problems on smooth manifolds are formulated. Under the Guignard constraint qualification, local minimizers are shown to admit Lagrange multipliers. The linear independence, Mangasarian-Fromovitz, and Abadie constraint qualifications are also formulated, and the chain “LICQ implies MFCQ implies ACQ implies GCQ” is proved. Moreover, classical connections between these constraint qualifications and the set of Lagrange multipliers are established, which parallel the results in Euclidean space. The constrained Riemannian center of mass on the sphere serves as an illustrating numerical example.
Prior publicationsfor a comprehensive list of publications see ronnybergmann.net/publications.html.
The following Links mostly refer to german pages.
Winter Term 2018
- Computergestützte Mathematik
- Organizer of the exercises and Tutor
- Höhere Mathematik III (If, Ph, ET)
- Linear Programs on Manifolds
- Optimization on Manifolds in Julia.
- Differential Equations on Manifolds
Topics for Bachelor- and Master Thesis
If you are interested in writing a thesis within optimization, manifolds, variational methods, please write an e-mail to an ronny,bergmann@....