An 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 compl...

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Bibliographic Details
Published in:International journal of computer mathematics 2021-02, Vol.98 (2), p.414-433
Main Authors: Kheirfam, B., Sangachin, M. Mohamadi
Format: Article
Language:English
Subjects:
9C22
Algorithms
Iterative methods
Optimization
polynomial complexity
predictor-corrector interior-point method
Predictor-corrector methods
Semidefinite optimization
wide neighbourhood
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Summary: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.
ISSN:0020-7160
1029-0265
DOI:10.1080/00207160.2020.1748604