A wide neighbourhood predictor-corrector infeasible-interior-point algorithm for symmetric cone programming - Shahraki, M. Sayadi; Mansouri, H.; Delavarkhalafi, A. (Optimization methods & software, 2022)
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 $ \mathcal {N}_∞ ^- $ N ∞ − , it does not necessarily stay within it but must stay within the wider neighbourhood $ \mathcal {N}(τ,\, β ) $ N ( τ , β ) . We prove that, besides the predictor step, each corrector step also reduces the duality gap by a rate of $ 1-\frac {1}{O\left (\sqrt {r}\right )} $ 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.