A Mehrotra predictor-corrector interior-point algorithm for semidefinite optimization

This paper proposes a second-order Mehrotra-type predictor-corrector feasible interior-point algorithm for semidefinite optimization problems. In each iteration, the algorithm computes the Newton search directions through a new form of combination of the predictor and corrector directions. Using the Ai-Zhang wide neighborhood for linear complementarity problems, it is shown that the complexity bound of the algorithm is O(root nlog epsilon(-1)) for the Nesterov Todd search direction and O(root nlog epsilon(-1)) for the Helmberg-Kojima-Monteiro search directions.