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

该项目的目的是为非线性流形上的等式约束问题开发鲁棒有效的优化方法。这种扩展的框架产生额外的灵活性，利用非线性问题的结构。我们将把现有的仿射协变复合步长方法扩展到流形的情况，并利用其不变性的优点。我们将专注于两个典型的应用程序，这也可以作为测试用例，以不断评估和改进我们的算法。第一个将是一个内点方法的建设，通过使用黎曼结构的正锥，第二个应用程序将考虑优化问题，涉及Cosserat棒。

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.