A primal-dual predictor-corrector interior-point method for symmetric cone programming with O(r log E-1) iteration complexity

In this paper,we propose a new predictor-corrector interior-point method for symmetric cone programming. This algorithm is based on a wide neighbourhood and the Nesterov-Todd direction. We prove that, besides the predictor steps, each corrector step also reduces the duality gap by a rate of , where r is the rank of the associated Euclidean Jordan algebras. In particular, the complexity bound is , where is a given tolerance. To our knowledge, this is the best complexity result obtained so far for interior-point methods with a wide neighbourhood over symmetric cones. The numerical results show that the proposed algorithm is effective.