A long-step feasible predictor–corrector interior-point algorithm for symmetric cone optimization

In this paper, we present a feasible predictor–corrector interior-point method for symmetric cone optimization problem in the large neighbourhood of the central path. The method is generalization of Ai-Zhang's predictor–corrector algorithm to the symmetric cone optimization problem. Starting with a feasible point (Formula presented.) in given large neighbourhood of the central path, the algorithm still terminates in at most (Formula presented.) iterations. This matches the best known iteration bound that is usually achieved by short-step methods, thereby, closing the complexity gap between long- and short-step interior-point methods for symmetric cone optimization. The preliminary numerical results on a selected set of NETLIB problems show advantage of the method in comparison with the version of the algorithm that is not based on the predictor–corrector scheme.