A full NT-step infeasible interior-point algorithm for semidefinite optimization

In this paper, a full Nesterov–Todd‐step infeasible interior‐point algorithm is presented for semidefinite optimization (SDO) problems. In contrast of some classical interior‐point algorithms for SDO problems, this algorithm does not need to perform computationally expensive calculations for centering steps which are needed for classical interior‐point methods. The convergence analysis of the algorithm is shown and it is also proved that the complexity bound of the algorithm coincides with the currently best iteration bound obtained by infeasible interior‐point algorithms for this class of optimization problems.