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

ABSTRACTIn 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 (x0,y0,s0) in given large neighbourhood of the central path, the algorithm still terminates in at most Orlog⁡(Tr(x0∘s0)/e) 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.