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Target Directions for Primal-Dual Interior-Point Methods for
Self-Scaled Conic Programming

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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. In the linear programming literature there exists a
unifying framework for the analysis of various important classes of
interior-point algorithms, known under the name of target-following
algorithms. This article is a step towards combining these two
unifying theories in that we develop an infinite new family of Newton
directions for self-scaled conic programming which inherit the
properties of the search-direction that made target-following
algorithms possible in the LP case. These so-called target directions
are close relatives of the Nesterov-Todd direction and lend themselves
to the construction of predictor-corrector methods. Moreover, target
directions are closely connected to the notion of weighted analytic
centers.
Numerical Analysis Report DAMTP 1999/NA15, Department of
Applied Mathematics and Theoretical Physics, Silver Street, Cambridge,
England CB3 9EW.

Contact: rah48@damtp.cam.ac.uk