A variational problem on Stiefel manifolds

A variational problem on Stiefel manifolds

In their paper on discrete analogues of some classical systems such as the rigid body and the geodesic flow on an ellipsoid, Moser and Veselov introduced their analysis in the general context of flows on Stiefel manifolds. We consider here a general class of continuous time, quadratic cost, optimal control problems on Stiefel manifolds, which in the extreme dimensions again yield these classica...

Global optimization on Stiefel manifolds — some particular problem instances ∗

Optimization on Stiefel manifolds was discussed by Rapcsák in earlier papers. There, some numerical methods of global optimization are dealt with and tested on Stiefel manifolds. In the paper the structure of the optimizer points is given in some particular problem instances and for a special form of a quadratic problem defined on a Stiefel manifold. Some reduction tricks and results are obtain...

Rolling Stiefel manifolds

In this paper rolling maps for real Stiefel manifolds are studied. Real Stiefel manifolds being the set of all orthonormal k-frames of an n-dimensional real Euclidean space are compact manifolds. They are considered here as rigid bodies embedded in a suitable Euclidean space such that the corresponding Euclidean group acts on the rigid body by rotations and translations in the usual way. We der...

Notes on Optimization on Stiefel Manifolds

Homogeneous Einstein metrics on Stiefel manifolds

A Stiefel manifold VkR n is the set of orthonormal k-frames inR, and it is diffeomorphic to the homogeneous space SO(n)/SO(n−k). We study SO(n)-invariant Einstein metrics on this space. We determine when the standard metric on SO(n)/SO(n−k) is Einstein, and we give an explicit solution to the Einstein equation for the space V2R.