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Nonsmooth Riemannian Optimization with Applications to Sphere Packing and Grasping

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Lagrangian and Hamiltonian Methods for Nonlinear Control 2006

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 366))

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.

Partially supported by the German Research Foundation under grant KONNEW HE 1858/10-1

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Author information

Authors and Affiliations

  1. Institute of Mathematics, University of Würzburg, Am Hubland, 97074, Würzburg, Germany

    Gunther Dirr, Uwe Helmke & Christian Lageman

Authors
  1. Gunther Dirr
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  2. Uwe Helmke
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  3. Christian Lageman
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Editor information

Editors and Affiliations

  1. Mechanical Engineering Department, University of California at Santa Barbara, 2338 Engineering Bldg II, Santa Barbara, CA, 93106-5070, USA

    Francesco Bullo

  2. Department of Mechanical Science and Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8603, Japan

    Kenji Fujimoto

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Dirr, G., Helmke, U., Lageman, C. (2007). Nonsmooth Riemannian Optimization with Applications to Sphere Packing and Grasping. In: Allgüwer, F., et al. Lagrangian and Hamiltonian Methods for Nonlinear Control 2006. Lecture Notes in Control and Information Sciences, vol 366. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73890-9_2

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  • DOI: https://doi.org/10.1007/978-3-540-73890-9_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73889-3

  • Online ISBN: 978-3-540-73890-9

  • eBook Packages: EngineeringEngineering (R0)

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