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.
J Optim Theory Appl Published online 25 April 2008