Riemannian preconditioning

This paper exploits a basic connection between sequential quadratic programming and Riemannian gradient optimization to address the general question of selecting a metric in Riemannian optimization, in particular when the Riemannian structure is sought on a quotient manifold. The proposed method is shown to be particularly insightful and efficient in quadratic optimization with orthogonality and/or rank constraints, which covers most current applications of Riemannian optimization in matrix manifolds.Belgium Science Policy Office, FNRS (Belgium)This is the author accepted manuscript. The final version is available from The Society for Industrial and Applied Mathematics via http://dx.doi.org/10.1137/14097086