Nonsmooth Riemannian Optimization with Applications to Sphere Packing and Grasping

  • Gunther Dirr
  • Uwe Helmke
  • Christian Lageman
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 366)


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.


Riemannian Manifold Descent Direction Sphere Packing Grassmann Manifold Chordal Distance 
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© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Gunther Dirr
    • 1
  • Uwe Helmke
    • 1
  • Christian Lageman
    • 1
  1. 1.Institute of MathematicsUniversity of WürzburgWürzburgGermany

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