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

J. X. Cruz Neto (), O. P. Ferreira (), P. R. Oliveira () and R. C. M. Silva ()
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J. X. Cruz Neto: Universidade Federal do Piauí
O. P. Ferreira: Universidade Federal de Goiás
P. R. Oliveira: Universidade Federal do Rio de Janeiro
R. C. M. Silva: Universidade Federal de Amazonas

Journal of Optimization Theory and Applications, 2008, vol. 139, issue 2, No 2, 227-242

Abstract: 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 (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-008-9422-2

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