Abstract
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.
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Hauser, R. The Nesterov–Todd Direction and Its Relation to Weighted Analytic Centers. Found Comput Math 4, 1–40 (2004). https://doi.org/10.1007/s10208-000-0009-z
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DOI: https://doi.org/10.1007/s10208-000-0009-z