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A wide neighborhood predictor-infeasible corrector interior-point algorithm for linear optimization

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Abstract

In this paper, we propose a theoretical framework of a predictor-corrector interior-point method for linear optimization based on the one-norm wide neighborhood of the central path, focusing on infeasible corrector steps. Here, we call the predictor-infeasible corrector algorithm. At each iteration, the proposed algorithm computes an infeasible corrector step in addition to the Ai-Zhang search directions and considers the Newton direction as a linear combination of these directions. We represent the complexity analysis of the algorithm and conclude that its iteration bound is \({\mathcal {O}}(n\log \varepsilon ^{-1})\). To our knowledge, this is the best complexity result up to now for infeasible interior-point methods based on these kinds of search directions. The complexity bound obtained here is the same as small neighborhood infeasible interior point algorithms.

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Acknowledgements

We thank the editor and the anonymous reviewers for the valuable suggestions that improved the presentation of the paper. The authors are also thankful for the support of the Azarbaijan Shahid Madani University.

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Kheirfam, B., Nasrollahi, A. A wide neighborhood predictor-infeasible corrector interior-point algorithm for linear optimization. Optim Lett 14, 2549–2563 (2020). https://doi.org/10.1007/s11590-020-01573-4

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