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. Key words. symmetric cones, self-scaled cones, primal-dual methods, interior-point methods, weighted analytic centers, target-following methods, convex programming, self-scaled programming, linear programming, semidefinite programming, second-order cone programming, quadratic programming.
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