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Research Group Numerical Mathematics (Partial Differential Equations)
PD Dr. Ronny Bergmann

PD Dr. Ronny Bergmann

Phone:
+49 371 531 36098
Fax:
+49 371 531 836098
Office:
Reichenhainer Str. 41, Office 609 (C47.609)
Scholar:
Secretary:
Anne-Kristin Glanzberg, Office 607, Phone +49 371 531 22500
Postal address:
TU Chemnitz, Faculty of Mathematics, 09107 Chemnitz, Germany
Office Hours:
any time when present
since 04/2018
member of research group Numerical Mathematics (Partial Differential Equations) of Prof. Dr. R. Herzog
01/2018
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
06/2013
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.
09/2009
master's degree in computer science, Institut für Mathematik, Universität zu Lübeck.
10/2004 — 09/2009
studies of computer science at Universität zu Lübeck
Further Links

Preprints

2018

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 publications

for a comprehensive list of publications see ronnybergmann.net/publications.html.