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A New Primal–Dual Predictor–Corrector Interior-Point Method for Linear Programming Based on a Wide Neighbourhood

Author

Listed:
  • M. Sayadi Shahraki

    (Shahrekord University)

  • H. Mansouri

    (Shahrekord University)

  • M. Zangiabadi

    (Shahrekord University)

Abstract

In this paper, we propose a new predictor–corrector interior-point algorithm for linear programming based on a wide neighbourhood. In each iteration, the algorithm computes the Ai-Zhang’s predictor direction (SIAM J. Optim. 16(2):400–417, 2005) and a new corrector direction, in an attempt to improve its performance. We drive that the duality gap reduces in both predictor and corrector steps. Moreover, we also prove that the complexity of the algorithm coincides with the best iteration bound for small neighbourhood algorithms. Finally, some numerical experiments are provided which reveal capability and effectiveness of the proposed method.

Suggested Citation

  • M. Sayadi Shahraki & H. Mansouri & M. Zangiabadi, 2016. "A New Primal–Dual Predictor–Corrector Interior-Point Method for Linear Programming Based on a Wide Neighbourhood," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 546-561, August.
    • Handle: RePEc:spr:joptap:v:170:y:2016:i:2:d:10.1007_s10957-016-0927-9
    DOI: 10.1007/s10957-016-0927-9
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    References listed on IDEAS

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    1. Shinji Mizuno & Michael J. Todd & Yinyu Ye, 1993. "On Adaptive-Step Primal-Dual Interior-Point Algorithms for Linear Programming," Mathematics of Operations Research, INFORMS, vol. 18(4), pages 964-981, November.
    2. Terlaky, Tamas, 2001. "An easy way to teach interior-point methods," European Journal of Operational Research, Elsevier, vol. 130(1), pages 1-19, April.
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