Abstract
In this paper, we present an improved version of the infeasible-interior-point method for linear optimization introduced by Roos (SIAM J Optim 16(4):1110–1136, 2006). Each main step of Roos’s algorithm is composed of one feasibility step and several centering steps. By using a new search direction, we prove that it is enough to take only one step in order to obtain a polynomial-time method. The iteration bound coincides with the currently best iteration bound for linear optimization problems.
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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 financial support. The authors were also partially supported by the Center of Excellence for Mathematics, University of Shahrekord, Shahrekord, Iran.
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Mansouri, H., Zangiabadi, M. & Arzani, M. A Modified Infeasible-Interior-Point Algorithm for Linear Optimization Problems. J Optim Theory Appl 166, 605–618 (2015). https://doi.org/10.1007/s10957-015-0719-7
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DOI: https://doi.org/10.1007/s10957-015-0719-7