Abstract
Short-step methods are an important class of algorithms for solving convex constrained optimization problems. In this short paper, we show that under very mild assumptions on the self-concordant barrier and the width of the \(\ell _2\)-neighbourhood, any short-step interior-point method is not strongly polynomial-time.
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Notes
After we finished this work, we were informed that a similar result has been obtained independently by another group [2] around the same time, via a different approach.
References
Allamigeon, X., Benchimol, P., Gaubert, S., Joswig, M.: Log-barrier interior point methods are not strongly polynomial. SIAM J. Appl. Algebra Geom. 2(1), 140–178 (2018)
Allamigeon, X., Gaubert, S., and Vandame, N.: No self-concordant barrier interior point method is strongly polynomial. arXiv preprint arXiv:2201.02186 (2022)
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Acknowledgements
The authors thank Defeng Sun, Kim-Chuan Toh and Stephen Wright for their helpful discussions.
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Zong, M., Lee, Y.T. & Yue, MC. Short-step methods are not strongly polynomial-time. Math. Program. (2023). https://doi.org/10.1007/s10107-023-02002-x
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DOI: https://doi.org/10.1007/s10107-023-02002-x