Convergence behavior of the central path for homogeneous and self-dual cones

Yinyu Ye

This is a small note resulted from the discussion among Nesterov, Todd and myself. The result is that the central path leads to a strict complementary solution if such a solution exists. This result may be interesting to many love-to-prove-superlinear-convergence researchers. This result holds for all homogeneous self-dual cones.