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An arc-search \({\mathcal {O}}(nL)\) infeasible-interior-point algorithm for linear programming

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Abstract

Arc-search interior-point methods have been proposed to capture the curvature of the central path using an approximation based on ellipse. Yang et al. (J Appl Math Comput 51(1–2):209–225, 2016) proved that an arc-search algorithm has the computational order of \({\mathcal {O}}(n^{5/4}L)\). In this paper, we propose an arc-search infeasible-interior-point algorithms and discuss its convergence analysis. We improve the polynomial bound from \({\mathcal {O}}(n^{5/4}L)\) to \({\mathcal {O}}(nL)\), which is at least as good as the best existing bound for infeasible-interior-point algorithms for linear programming. Numerical results indicate that the proposed method solved LP instances faster than the existing \({\mathcal {O}}(n^{5/4}L)\) method.

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Acknowledgements

Makoto Yamashita’s research was partially supported by JSPS KAKENHI (Grant Number: 15K00032).

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Authors and Affiliations

  1. US NRC, Office of Research, 21 Church Street, Rockville, MD, 20850, USA

    Yaguang Yang

  2. Department of Mathematical and Computing Science, Tokyo Institute of Technology, Tokyo, Japan

    Makoto Yamashita

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  1. Yaguang Yang
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  2. Makoto Yamashita
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Correspondence to Makoto Yamashita.

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Yang, Y., Yamashita, M. An arc-search \({\mathcal {O}}(nL)\) infeasible-interior-point algorithm for linear programming. Optim Lett 12, 781–798 (2018). https://doi.org/10.1007/s11590-017-1142-9

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  • DOI: https://doi.org/10.1007/s11590-017-1142-9

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