New complexity analysis of the primal–dual method for semidefinite optimization based on the Nesterov–Todd direction

Interior-point methods for semidefinite optimization have been studied intensively in recent times, due to their polynomial complexity and practical efficiency. In this paper, first we present some technical results about symmetric matrices. Then, we apply these results to give a unified analysis for both large update and small update interior-point methods for SDP based on the Nesterov–Todd direction.