A wide neighbourhood predictor–corrector infeasible-interior-point algorithm for symmetric cone programming. (2nd November 2022) - Shahraki, M. Sayadi; Mansouri, H.; Delavarkhalafi, A.
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 N ∞ −, it does not necessarily stay within it but must stay within the wider neighbourhood N ( τ, β ) . We prove that, besides the predictor step, each corrector step also reduces the duality gap by a rate of 1 − 1 O ( r ), 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.