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

Abstract

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 \({O(r^{3/2}\,\log\epsilon^{-1})}\) for the NT methods, and \({O(r^{2}\,\log\epsilon^{-1})}\) for the XS and SX methods, where r is the rank of the associated Euclidean Jordan algebra and \({\epsilon\,{ > }\,0}\) is a given tolerance. If the staring point is strictly feasible, then the corresponding bounds can be reduced by a factor of r3/4. The theory of Euclidean Jordan algebras is a basic tool in our analysis.