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Central Paths in Semidefinite Programming, Generalized Proximal-Point Method and Cauchy Trajectories in Riemannian Manifolds

  • J. X. da Cruz Neto
  • O. P. Ferreira
  • P. R. Oliveira
  • R. C. M. Silva
Article

Abstract

The relationships among the central path in the context of semidefinite programming, generalized proximal-point method and Cauchy trajectory in a Riemannian manifolds is studied in this paper. First, it is proved that the central path associated to a general function is well defined. The convergence and characterization of its limit point is established for functions satisfying a certain continuity property. Also, the generalized proximal-point method is considered and it is proved that the correspondingly generated sequence is contained in the central path. As a consequence, both converge to the same point. Finally, it is proved that the central path coincides with the Cauchy trajectory in a Riemannian manifold.

Keywords

Central path Generalized proximal-point methods Cauchy trajectory Semidefinite programming Riemannian manifolds 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • J. X. da Cruz Neto
    • 1
  • O. P. Ferreira
    • 2
  • P. R. Oliveira
    • 3
  • R. C. M. Silva
    • 4
  1. 1.DMUniversidade Federal do PiauíTeresinaBrazil
  2. 2.IMEUniversidade Federal de GoiásGoiâniaBrazil
  3. 3.COPPE-SistemasUniversidade Federal do Rio de JaneiroRio de JaneiroBrazil
  4. 4.DM, ICEUniversidade Federal de AmazonasManausBrazil

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