Accelerated First-order Methods for Geodesically Convex Optimization on Riemannian Manifolds

In this paper, we propose an accelerated first-order method for geodesically convex optimization, which is the generalization of the standard Nesterov's accelerated method from Euclidean space to nonlinear Riemannian space. We first derive two equations and obtain two nonlinear operators for geodesically convex optimization instead of the linear extrapolation step in Euclidean space.