A new second‐order corrector interior‐point algorithm for semidefinite programming

In this paper, we propose a second‐order corrector interior‐point algorithm for semidefinite programming (SDP). This algorithm is based on the wide neighborhood. The complexity bound is $O(\sqrt{n}L)$ for the Nesterov‐Todd direction, which coincides with the best known complexity results for SDP. To our best knowledge, this is the first wide neighborhood second‐order corrector algorithm with the same complexity as small neighborhood interior‐point methods for SDP. Some numerical results are provided as well.