Complexity analysis and numerical implementation of a new interior-point algorithm for semidefinite optimization

Abstract

We generalize Zhang and Xu's (2011) [22] interior point algorithm for linear optimization to semidefinite optimization problems in order to define a new search direction. The symmetrization of the search direction is based on the full Nesterov-Todd scaling scheme. Moreover, we show that the obtained algorithm solves the studied problem in polynomial time and that the short-step algorithm has the best-known iteration bound, namely $O(\sqrt{n}\log \frac{n}{\epsilon })$-iterations. Finally, we report a comparative numerical study to show the efficiency of our proposed algorithm.