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Riemannian preconditioning

Accepted version
Peer-reviewed

Repository DOI


Type

Article

Change log

Authors

Mishra, B 
Sepulchre, Rodolphe  ORCID logo  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

Volume Title

26

Publisher

Society for Industrial & Applied Mathematics (SIAM)
Sponsorship
Belgium Science Policy Office, FNRS (Belgium)