Nonsmooth riemannian optimization with applications to sphere packing and grasping

Abstract

This paper presents a survey on Riemannian geometry methods for smooth and nonsmooth constrained optimization. Gradient and subgradient descent algorithms on a Riemannian manifold are discussed. We illustrate the methods by applications from robotics and multi antenna communication. Gradient descent algorithms for dextrous hand grasping and for sphere packing problems on Grassmann manifolds are presented respectively. © Springer-Verlag Berlin Heidelberg 2007.