A full Nesterov-Todd-step feasible primal-dual interior point algorithm for convex quadratic semi-definite optimization

In this paper, a short-step feasible primal-dual path-following interior point algorithm is proposed for solving a convex quadratic semidefinite optimization (CQSDO) problem. The algorithm uses at each iteration full Nesterov-Todd (NT) steps to find an ∊-approximated solution of CQSDO. The favorable iteration bound, namely Onlogn∊ is obtained for short-step method and which is as good as the linear and semidefinite optimization analogue.