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Nesterov-Todd Directions are Newton Directions

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Raphael Hauser

The theory of self-scaled conic programming provides a unified
framework for the theories of linear programming, semidefinite
programming and convex quadratic programming with convex quadratic
constraints. The standard search directions for interior-point methods
applied to self-scaled conic programming problems are the so-called
Nesterov-Todd directions. In this article we show that these direction
fields are special cases of so-called target directions, a unifying
concept for primal-dual interior point methods for self-scaled conic
programming. In particular, this implies that Nesterov-Todd directions
derive from a Newton system.
Numerical Analysis Report DAMTP 1999/NA17, Department of
Applied Mathematics and Theoretical Physics, Silver Street,
Cambridge, England CB3 9EW.

Contact: rah48@damtp.cam.ac.uk