Tag: Riemannian Geometry

Uses tools from Riemannian geometry

Distributed localization algorithms

Imagine a wireless camera network, where each camera has a piece of local information, e.g., the pose of the object from a specific viewpoint or the relative poses with respect to the neighboring cameras. It is natural to look for distributed algorithms which merge all these local measurements into a single, globally consistent estimate. I […]

Distributed optimization on Riemannian manifolds

I worked on distributed optimization problems involving variables lying on non-linear spaces (that is, Riemannian manifolds) using extensions of gradient descent algorithms with fixed step size. I developed novel theoretical tools which significantly broadened the state of the art for determining sufficient conditions for global behaviors (algorithm convergence) using only local information. These tools have […]