Abstract
In this paper, we present a polynomial primal-dual interior-point algorithm for linear optimization based on a modified logarithmic barrier kernel function. Iteration bounds for the large-update interior-point method and the small-update interior-point method are derived. It is shown that the large-update interior-point method has the same polynomial complexity as the small-update interior-point method, which is the best known iteration bounds. Our result closes a long-existing gap in the theoretical complexity bounds for large-update interior-point method and small-update interior-point method.
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Acknowledgements
We are sincerely grateful to the editors and the anonymous referees for the careful reading and useful suggestions, which have improved the manuscript of the present version. This research was funded by Natural Science Foundation of Shandong Province (Grand No.ZR2020MA026).
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Liu, L., Hua, T. A polynomial interior-point algorithm with improved iteration bounds for linear optimization. Japan J. Indust. Appl. Math. 41, 739–756 (2024). https://doi.org/10.1007/s13160-023-00630-6
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DOI: https://doi.org/10.1007/s13160-023-00630-6