Optimization on Manifolds for the Numerical Solution of Equality Constrained Variational Problems

• Applicant: Professor Dr. Anton Schiela
• Subject Area: Mathematics
• Term: from 2016 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 318513007

Aim of the project is to develop robust and efficient optimization methods for equality constrained problems on nonlinear manifolds. This extended framework yields additional flexibility to exploit nonlinear problem structure. We will extend an existing affine covariant composite step method to the manifold case, and exploit the benefits of its invariance properties.We will focus on two prototypical applications, which also serve as test cases to continuously evaluate and improve our algorithms. The first will be the construction of an interior point method by using the Riemannian structure of the positive cone, the second application will consider optimization problems involving Cosserat rods.

• DFG Programme: Research Grants