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In this paper, we propose a new predictor–corrector infeasible-interior-point algorithm for symmetric cone programming. Each iterate always follows the usual wide neighbourhood, it does not necessarily stay within it but must stay within the wider neighbourhood. We prove that, besides the predictor step, each corrector step also reduces the duality gap by a rate of, where  r  is the rank of the associated Euclidean Jordan algebra. Moreover, we improve the theoretical complexity bound of an infeasible-interior-point method. Some numerical results are provided as well.

A wide neighbourhood predictor–corrector infeasible-interior-point algorithm for symmetric cone programming