  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.
