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Infeasible Interior-Point Methods for Linear Optimization Based on Large Neighborhood

Author

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  • Alireza Asadi

    (Delft University of Technology)

  • Cornelis Roos

    (Delft University of Technology)

Abstract

In this paper, we design a class of infeasible interior-point methods for linear optimization based on large neighborhood. The algorithm is inspired by a full-Newton step infeasible algorithm with a linear convergence rate in problem dimension that was recently proposed by the second author. Unfortunately, despite its good numerical behavior, the theoretical convergence rate of our algorithm is worse up to square root of problem dimension.

Suggested Citation

  • Alireza Asadi & Cornelis Roos, 2016. "Infeasible Interior-Point Methods for Linear Optimization Based on Large Neighborhood," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 562-590, August.
    • Handle: RePEc:spr:joptap:v:170:y:2016:i:2:d:10.1007_s10957-015-0826-5
    DOI: 10.1007/s10957-015-0826-5
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    References listed on IDEAS

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    1. Anstreicher, K., 1989. "A Combined Phase I - Phase Ii Scaled Potential Algorithm For Linear Programming," LIDAM Discussion Papers CORE 1989039, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Salahi, M. & Peyghami, M.R. & Terlaky, T., 2008. "New complexity analysis of IIPMs for linear optimization based on a specific self-regular function," European Journal of Operational Research, Elsevier, vol. 186(2), pages 466-485, April.
    3. Gu, G. & Zangiabadi, M. & Roos, C., 2011. "Full Nesterov-Todd step infeasible interior-point method for symmetric optimization," European Journal of Operational Research, Elsevier, vol. 214(3), pages 473-484, November.
    4. G. Gu & H. Mansouri & M. Zangiabadi & Y. Q. Bai & C. Roos, 2010. "Improved Full-Newton Step O(nL) Infeasible Interior-Point Method for Linear Optimization," Journal of Optimization Theory and Applications, Springer, vol. 145(2), pages 271-288, May.
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    Cited by:

    1. Fabio Vitor & Todd Easton, 2022. "Projected orthogonal vectors in two-dimensional search interior point algorithms for linear programming," Computational Optimization and Applications, Springer, vol. 83(1), pages 211-246, September.

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