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

J. X. da Cruz Neto (jxavier***at***ufpi.br)
O. P. Ferreira (orizon***at***mat.ufg.br)
P. R. Oliveira (poliveir***at***cos.ufrj.br)
R. C. M. Silva (rmesquita***at***ufam.edu.br)

Abstract: The relationships among central path in the context of semidefinite programming, generalized proximal point method and Cauchy trajectory in Riemannian manifolds is studied in this paper. First it is proved that the central path associated to the general function is well defined. The convergence and characterization of its limit point is established for functions satisfying a certain continuous property. Also, the generalized proximal point method is considered, and it is proved that the corresponding 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 the Riemannian manifold.

Keywords: central path, generalized proximal point methods, Cauchy trajectory, semidefinite programming, Riemannian manifold.

Category 1: Linear, Cone and Semidefinite Programming

Citation: J Optim Theory Appl Published online 25 April 2008

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Entry Submitted: 02/02/2006
Entry Accepted: 02/02/2006
Entry Last Modified: 05/15/2008

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