Riemannian BFGS Algorithm with Applications

Chunhong Qi, Kyle Gallivan, Pierre-Antoine Absil

In this paper, we present a retraction-based Riemannian BFGS approach (RBFGS) for optimization on a Riemannian manifold. Of particular interest is the choice of transport used to move information between tangent spaces and the different ways of implementing the RBFGS algorithm. We consider parallel translation along a geodesic and vector transport by projection on the unit sphere and the compact Stiefel manifold.