An Efficient BFGS Algorithm for Riemannian Optimization

In this paper, we present a convergence result for Riemannian line-search methods that ensures superlinear convergence. We also present a theory of building vector transports on submanifolds of R n and discuss its use to assess convergence conditions and computational effi ciency of the resulting Riemannian optimization algorithms. We illustrate performance and check predictions of our theory using a version of a Riemannian BFGS algorithm we proposed earlier.