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The Nesterov-Todd direction and its relation to weighted analytic centers. (English) Zbl 1144.90459

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.

MSC:

90C25 Convex programming
34E10 Perturbations, asymptotics of solutions to ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
90C60 Abstract computational complexity for mathematical programming problems
90C05 Linear programming
90C20 Quadratic programming

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