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

Abstract

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 (√ n log ε −1 ) for the Nesterov-Todd search direction and O ( n log ε −1 ) for the Helmberg-Kojima-Monteiro search directions.