中文摘要：

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(n3/2log（X0）T·S0/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(n3/2log（X0）T·S0/ε), which coincides with the currently best iteration bound of Mehrotra-type predictor-corrector algorithm for semidefinite optimization.

英文摘要：

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 had3/2 0 T 0O（nlog（X）gS/e）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 to0 0O（nlog XgS/e）,which coincides with the currently best iteration bound of Mehrotra-type predictor-corrector algorithm for semidefinite optimization.