Square-root fields and the V-space approach to primal-dual interior-point methods for self-scaled conic programming

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 a convenient framework for the analysis of primal-dual interior-point methods is known as the ``V-space''approach. Various generalizations of this framework have recently been proposed for semidefinite and self-scaled conic programming. We propose such a generalization that inherits all the properties that made this approach a successful analytical tool in the linear programming case. Contrary to certain other generalizations, the objects at the center of our own approach, so-called square-root fields, are endowed with a differential structure that plays a crucial role in the asymptotic analysis of primal-dual algorithms.

Numerical Analysis Report DAMTP 1999/NA14, Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge, CB3 9EW.

Contact: rah48@damtp.cam.ac.uk