Riemannian preconditioning
Accepted version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Mishra, B
Sepulchre, Rodolphe https://orcid.org/0000-0002-7047-3124
Abstract
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.
Description
Keywords
Riemannian optimization, sequential quadratic programming, metric tuning, quotient manifold, Grassmann, low rank, generalized eigenvalue problem, Lyapunov equation
Journal Title
SIAM Journal on Optimization
Conference Name
Journal ISSN
1052-6234
1095-7189
1095-7189
Volume Title
26
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Publisher DOI
Sponsorship
Belgium Science Policy Office, FNRS (Belgium)