Riemannian preconditioning

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.

References in corpus (5)

• Manopt, a Matlab toolbox for optimization on manifolds
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• Low-rank optimization for distance matrix completion
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• New vector transport operators extending a Riemannian CG algorithm to generalized Stiefel manifold with low-rank applications
• Output-feedback Synthesis Orbit Geometry: Quotient Manifolds and LQG Direct Policy Optimization
• Inductive Geometric Matrix Midranges
• A Riemannian gradient descent method for optimization on the indefinite Stiefel manifold
• On the analysis of optimization with fixed-rank matrices: a quotient geometric view
• A generalized canonical metric for optimization on the indefinite Stiefel manifold