Riemannian preconditioning

Riemannian preconditioning


B. Mishra and R. Sepulchre


The 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.



Extreme eigenspace computation.
Low-rank solutions to Lyapunov equations.