A new second-order Mehrotra-type predictor-corrector algorithm for SDO

In Zhang’s recent works, a second-order Mehrotra-type predictor-corrector algorithm for linear optimization was extended to semidefinite optimization and derived that the algorithm for semidefinite optimization had O(n ^3/2log(X ⁰)^T?S ⁰/ε) iteration complexity based on the NT direction as Newton search direction. In this paper, we extend the second-order Mehrotra-type predictor-corrector algorithm for linear optimization to semidefinite optimization and discuss the polynomial convergence of the algorithm by modifying the corrector direction and new iterates. It is proved that the iteration complexity is reduced to O(nlogX ⁰?S ⁰/ε), which coincides with the currently best iteration bound of Mehrotra-type predictor-corrector algorithm for semidefinite optimization.