An predictor–corrector interior-point algorithm for semidefinite optimization based on a wide neighbourhood

Abstract

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.

Keywords:

• Semidefinite optimization
• predictor–corrector interior-point method
• wide neighbourhood
• polynomial complexity

2010 Mathematics Subject Classifications:

• 9C22
• 90C51

Acknowledgments

The authors would like to thank the Editors and the anonymous referees for their useful comments and suggestions, which helped to improve the presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

B. Kheirfam  http://orcid.org/0000-0001-7928-2618