Hajg Jasa

Ronny Bergmann, Hajg Jasa, Paula John et al.

We consider the proximal gradient method on Riemannian manifolds for functions that are possibly not geodesically convex. Starting from the forward-backward-splitting, we define an intrinsic variant of the proximal gradient method that uses proximal maps defined on the manifold and therefore does not require or work in the embedding. We investigate its convergence properties and illustrate its numerical performance, particularly for nonconvex or nonembedded problems that are hence out of reach for other methods.

Jacob R. Goodman, Hajg Jasa

We introduce a rank-one Riemannian cometric update inducing a modification of the Riemannian metric that makes specific directions of motion cheaper to travel along. We establish basic completeness properties of this reward metric, and give an explicit characterization of its Levi--Civita connection. We propose a preconditioned trajectory-tracking strategy by adding the connection-difference term to a standard intrinsic PD control, and illustrate the construction on a connection control-affine system on the Special Euclidean group with a maze navigation experiment. When the nominal trajectory is an integral curve of the vector field used to define the reward metric, our methodology improves the overall tracking, which is demonstrated through simulation results.