Central Paths in Semidefinite Programming, Generalized Proximal-Point Method and Cauchy Trajectories in Riemannian Manifolds |
| |
| Authors: | J X da Cruz Neto O P Ferreira P R Oliveira R C M Silva |
| |
| Institution: | (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 |
| |
| 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. |
| |
| Keywords: | Central path Generalized proximal-point methods Cauchy trajectory Semidefinite programming Riemannian manifolds |
| 本文献已被 SpringerLink 等数据库收录！ |
|
