Modified polynomial-time full-NT-step infeasible interior-point algorithm for symmetric optimisation

In this paper, we improve the full Nesterov‐Todd (NT)‐step infeasible‐interior‐point algorithm for symmetric optimisation of Gu et al. (2011). Our proposed algorithm differs from Gu et al.'s algorithm such that it has the advantage that no centring steps are needed. In each main iteration of Gu et al.'s algorithm, one feasibility and a few centring steps are needed to get feasible iterates for a pair of perturbed problems, close enough to its central path. In this paper, we perform only one full‐NT‐step in each main iteration of the algorithm. Despite eliminating the centring steps, the complexity bound of our algorithm matches the best obtained one for symmetric optimisation.