The Nesterov-Todd direction and its relation to weighted analytic centers (Q1879036)

The subject of this paper concerns differential-geometric properties of the Nesterov--Todd search direction for linear optimization over symmetric cones. In particular, we investigate the rescaled asymptotics of the associated flow near the central path. Our results imply that the Nesterov--Todd direction arises as the solution of a Newton system defined in terms of a certain transformation of the primal-dual feasible domain. This transformation has especially appealing properties which generalize the notion of weighted analytic centers for linear programming.