An O(√nL) predictor-corrector interior-point algorithm for semidefinite optimization based on a wide neighbourhood

In this paper, we propose a new predictor-corrector interior-point algorithm for semidefinite optimization based on a wide neighbourhood of the central path. We show that, in addition to the predictor step, each corrector step decreases the duality gap as well. We also prove that the iteration complexity of the proposed algorithm coincides with the best iteration bound for small neighbourhood algorithms that use the Nesterov-Todd direction. Finally, some numerical results are provided as well.

Automated summary

This paper introduces a new predictor-corrector interior-point algorithm for semidefinite optimization, demonstrating that both predictor and corrector steps contribute to decreasing the duality gap. The proposed algorithm's iteration complexity aligns with the best iteration bound for small neighbourhood algorithms using the Nesterov-Todd direction, and numerical results are provided as well.