In this paper a weighted short-step primal-dual interior-point algorithm for
linear optimization over symmetric cones is proposed that uses new search directions.
The algorithm uses at each interior-point iteration a full Nesterov-Todd step and the
strategy of the central path to obtain a solution of symmetric optimization. We establish
the iteration bound for the algorithm, which matches the currently best-known
iteration bound for these methods, and prove that the algorithm is quadratically convergent.