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

Abstract

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.