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Nonsmooth Riemannian optimization with applications to sphere packing and grasping. (English) Zbl 1151.53029
Bullo, Francesco (ed.) et al., Lagrangian and Hamiltonian methods for nonlinear control 2006. Proceedings from the 3rd IFAC workshop, Nagoya, Japan, July 19–21, 2006. Berlin: Springer (ISBN 978-3-540-73889-3/pbk). Lecture Notes in Control and Information Sciences 366, 29-45 (2007).
Riemannian geometry methods have recently contributed to developing optimization algorithms by exploiting the intrinsic geometric structure of the constraint set. In the present survey, gradient and subgradient descent algorithms on a Riemannian manifold are discussed with applications to robotics and multi antenna communication. Finally, gradient descent algoritms for dextrous hand grasping and sphere packing problems on Grassmann manifolds are given.
For the entire collection see [Zbl 1119.93006].

MSC:
53C20 Global Riemannian geometry, including pinching
58C05 Real-valued functions on manifolds
53A17 Differential geometric aspects in kinematics
52C17 Packing and covering in \(n\) dimensions (aspects of discrete geometry)
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