Central Paths in Semidefinite Programming, Generalized Proximal-Point Method and Cauchy Trajectories in Riemannian Manifolds |
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| Authors: | J. X. da Cruz Neto O. P. Ferreira P. R. Oliveira R. C. M. Silva |
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| Affiliation: | (1) DM, Universidade Federal do Piauí, Teresina, PI, 64049-500, Brazil;(2) IME, Universidade Federal de Goiás, Goiania, GO, 74001-970, Brazil;(3) COPPE-Sistemas, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, 21945-970, Brazil;(4) DM, ICE, Universidade Federal de Amazonas, Manaus, AM, 69077-000, Brazil |
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| 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. This work was supported in part by CNPq Grant 302618/2005-8, by PRONEX(CNPq), CAPES-PICDT and FUNAPE/UFG. |
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| Keywords: | Central path Generalized proximal-point methods Cauchy trajectory Semidefinite programming Riemannian manifolds |
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