Abstract
In this paper, we present a primal–dual interior point method for linear optimization problems based on a new efficient kernel function with a trigonometric barrier term. We derive the complexity bounds for large and small-update methods, respectively. We obtain the best known complexity bound for large update, which improves significantly the so far obtained complexity results based on a trigonometric kernel function given by Peyghami et al. The results obtained in this paper are the first to reach this goal.
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The authors are very grateful and would like to thank the anonymous referees for their suggestions and helpful comments, which significantly improved the presentation of this paper.
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Communicated by Suliman Saleh Al-Homidan.
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Bouafia, M., Benterki, D. & Yassine, A. An Efficient Primal–Dual Interior Point Method for Linear Programming Problems Based on a New Kernel Function with a Trigonometric Barrier Term. J Optim Theory Appl 170, 528–545 (2016). https://doi.org/10.1007/s10957-016-0895-0
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DOI: https://doi.org/10.1007/s10957-016-0895-0