Polynomial complexity of an interior point algorithm with a second order corrector step for symmetric cone programming

In this paper, we propose a second order interior point algorithm for symmetric cone programming using a wide neighborhood of the central path. The convergence is shown for commutative class of search directions. The complexity bound is O(r^3/2log ϵ^-1) for the NT methods, and O(r²log ϵ^-1) for the XS and SX methods, where r is the rank of the associated Euclidean Jordan algebra and ϵ >0 is a given tolerance. If the staring point is strictly feasible, then the corresponding bounds can be reduced by a factor of r ^3/4. The theory of Euclidean Jordan algebras is a basic tool in our analysis.