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.
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Acknowledgments
The authors would like to thank the anonymous referees for their useful comments and suggestions, which helped to improve the presentation of this paper. The authors also wish to thank Shahrekord University for the financial support. The authors were also partially supported by the Center of Excellence for Mathematics, University of Shahrekord, Shahrekord, Iran.
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All the authors are partially supported by Shahrekord University. We declare no conflict of interest.
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Sayadi Shahraki, M., Mansouri, H. & Zangiabadi, M. A New Primal–Dual Predictor–Corrector Interior-Point Method for Linear Programming Based on a Wide Neighbourhood . J Optim Theory Appl 170, 546–561 (2016). https://doi.org/10.1007/s10957-016-0927-9
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DOI: https://doi.org/10.1007/s10957-016-0927-9