In linear programming, the central path is known to converge to the analytic center of the set of optimal solutions. Recently, it has been shown that this is not necessarily true for linear semidefinite programming in the absence of strict complementarity. The present paper deals with the formulation of a convex problem whose solution defines the limit point of the central path. This problem is closely related to the analytic center problem for the set of optimal solutions. In the strict complementarity case the problems are shown to coincide.
Report TRITA-MAT-02-OS12, Department of Mathematics, Royal Institute of Technology (KTH), Stockholm, Sweden, June 2002.