Subgradient Algorithm on Riemannian Manifolds

  • O. P. Ferreira
  • P. R. Oliveira
Article

Abstract

The subgradient method is generalized to the context of Riemannian manifolds. The motivation can be seen in non-Euclidean metrics that occur in interior-point methods. In that frame, the natural curves for local steps are the geodesies relative to the specific Riemannian manifold. In this paper, the influence of the sectional curvature of the manifold on the convergence of the method is discussed, as well as the proof of convergence if the sectional curvature is nonnegative.

Nondifferentiable optimization convex programming subgradient methods Riemannian manifolds 

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Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • O. P. Ferreira
    • 1
  • P. R. Oliveira
    • 2
  1. 1.Instituto de Matemática e EstatisticaUniversidade Federal de GoiásGoiânia, GoiásBrazil
  2. 2.Programa de Engenharia de Sistemas e Computação, COPPEUniversidade Federal do Rio de JaneiroRio de JaneiroBrazil

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