We extend the target map, together with the weighted barriers and the notions of weighted analytic centers, from linear programming to general convex conic programming. This extension is obtained from a novel geometrical perspective of the weighted barriers, that views a weighted barrier as a weighted sum of barriers for a strictly decreasing sequence of faces. Using the Euclidean Jordan-algebraic structure of symmetric cones, we give an algebraic characterization of a strictly decreasing sequence of its faces, and specialize this target map to produce a computationally-tractable target-following algorithm for symmetric cone programming. The analysis is made possible with the use of triangular automorphisms of the cone, a new tool in the study of symmetric cone programming. As an application of this algorithm, we demonstrate that starting from any given any pair of primal-dual strictly feasible solutions, the primal-dual central path of a symmetric cone program can be efficiently approximated.
Research Report, January 2011, Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore