Nesterov-Todd Directions are Newton Directions

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.