Abstract
In this paper, we propose a primal–dual interior-point method for semidefinite optimization problems. The algorithm is based on a new class of search directions and the Ai-Zhang’s wide neighborhood for monotone linear complementarity problems. The theoretical complexity of the new algorithm is calculated. It is investigated that the proposed algorithm has polynomial iteration complexity \(O(\sqrt{n}L)\) and coincides with the best known iteration bound for semidefinite optimization problems.
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Acknowledgments
The authors would like to thank the anonymous referees for their useful comments and suggestions, which helped to improve the presentation of this paper. The authors also wish to thank Shahrekord University for financial support. The authors were also partially supported by the Center of Excellence for Mathematics, University of Shahrekord, Shahrekord, Iran.
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Communicated by Andreas Fischer.
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Pirhaji, M., Mansouri, H. & Zangiabadi, M. An \(O\left(\sqrt{n}L\right)\) wide neighborhood interior-point algorithm for semidefinite optimization. Comp. Appl. Math. 36, 145–157 (2017). https://doi.org/10.1007/s40314-015-0220-9
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DOI: https://doi.org/10.1007/s40314-015-0220-9