Manifold optimization is an emerging field of contemporary optimization that constructs efficient and robust algorithms by exploiting the specific geometrical structure of the search space. In our case the search space takes the form of a manifold. 

Manifold optimization methods mainly focus on adapting existing optimization methods from the usual “easy-to-deal-with” Euclidean search spaces to manifolds whose local geometry can be defined e.g. by a Riemannian structure. In this way the form of the adapted algorithms can stay unchanged. However,...

Manifold optimization is an emerging field of contemporary optimization that constructs efficient and robust algorithms by exploiting the specific geometrical structure of the search space. In our case the search space takes the form of a manifold. 

Manifold optimization methods mainly focus on adapting existing optimization methods from the usual “easy-to-deal-with” Euclidean search spaces to manifolds whose local geometry can be defined e.g. by a Riemannian structure. In this way the form of the adapted algorithms can stay unchanged. However,...