  We propose a Riemannian version of Nesterov's Accelerated Gradient algorithm
(RAGD), and show that for geodesically smooth and strongly convex problems,
within a neighborhood of the minimizer whose radius depends on the condition
number as well as the sectional curvature of the manifold, RAGD converges to
the minimizer with acceleration. Unlike the algorithm in (Liu et al., 2017)
that requires the exact solution to a nonlinear equation which in turn may be
intractable, our algorithm is constructive and computationally tractable. Our
proof exploits a new estimate sequence and a novel bound on the nonlinear
metric distortion, both ideas may be of independent interest.
