A Wide Neighborhood Second-order Predictor-corrector Interior-point Algorithm for Semidefinite Optimization with Modified Corrector Directions

Abstract

In this paper, we present a new second-order predictor-corrector interior-point method for semidefinite optimization. The algorithm is based on the wide neighborhood of the central path and modified corrector directions. In the corrector step, we derive the step size and corrector directions which guarantee that new iterate lies in the wide neighborhood. The iteration complexity bound is $O\left(\sqrt{n}\log \frac{X^o•S^o}{\varepsilon }\right)$ for the Nesterov-Todd direction, which coincides with the best known complexity results for semidefinite optimization. Some numerical results are provided as well.