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Improved Full-Newton Step O(nL) Infeasible Interior-Point Method for Linear Optimization

Author

Listed:
  • G. Gu

    (Delft University of Technology)

  • H. Mansouri

    (Shahrekord University)

  • M. Zangiabadi

    (Shahrekord University)

  • Y. Q. Bai

    (Shanghai University)

  • C. Roos

    (Delft University of Technology)

Abstract

We present several improvements of the full-Newton step infeasible interior-point method for linear optimization introduced by Roos (SIAM J. Optim. 16(4):1110–1136, 2006). Each main step of the method consists of a feasibility step and several centering steps. We use a more natural feasibility step, which targets the μ +-center of the next pair of perturbed problems. As for the centering steps, we apply a sharper quadratic convergence result, which leads to a slightly wider neighborhood for the feasibility steps. Moreover, the analysis is much simplified and the iteration bound is slightly better.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:145:y:2010:i:2:d:10.1007_s10957-009-9634-0
    DOI: 10.1007/s10957-009-9634-0
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    Citations

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    Cited by:

    1. G. Q. Wang & L. C. Kong & J. Y. Tao & G. Lesaja, 2015. "Improved Complexity Analysis of Full Nesterov–Todd Step Feasible Interior-Point Method for Symmetric Optimization," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 588-604, August.
    2. G. Q. Wang & Y. Q. Bai & X. Y. Gao & D. Z. Wang, 2015. "Improved Complexity Analysis of Full Nesterov–Todd Step Interior-Point Methods for Semidefinite Optimization," Journal of Optimization Theory and Applications, Springer, vol. 165(1), pages 242-262, April.
    3. 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.
    4. Behrouz Kheirfam, 2014. "A New Complexity Analysis for Full-Newton Step Infeasible Interior-Point Algorithm for Horizontal Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 853-869, June.
    5. H. Mansouri & M. Zangiabadi & M. Arzani, 2015. "A Modified Infeasible-Interior-Point Algorithm for Linear Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 605-618, August.
    6. Xiaoni Chi & Guoqiang Wang, 2021. "A Full-Newton Step Infeasible Interior-Point Method for the Special Weighted Linear Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 108-129, July.

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