Abstract:
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Optimization and inverse problems are most frequently formulated
in vector spaces. In some situations, however, a more natural
formulation is obtained on manifolds. Examples include problems
involving shapes and interfaces, as well as problems with
manifold-valued data such as normal vector fields or diffusion
tensors. In this presentation, we give an introduction into
optimization and inverse problems on manifolds. We touch upon
optimality conditions, algorithms and present numerical examples.