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Interior-Point Algorithms: Creation History, Research Results, Applications, and Prospects*

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Cybernetics and Systems Analysis Aims and scope

Abstract

The authors consider a family of interior-point algorithms for solving linear programming problems and provide the results of their theoretical substantiation. Subsets of algorithms that have a linear rate of convergence, asymptotically independent of the parameters of the problem being solved, and a subset of algorithms that lead to relatively interior points of the set of optimal solutions are identified. The history of the creation and development of the algorithms is described. New modifications of interior-point algorithms are presented, which contain the previously developed algorithms as a special case.

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Authors and Affiliations

  1. V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    T. V. Belykh

  2. Limnological Institute, Siberian Branch of the Russian Academy of Sciences, Irkutsk, Russia

    V. I. Zorkaltsev

Authors
  1. T. V. Belykh
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  2. V. I. Zorkaltsev
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Corresponding author

Correspondence to T. V. Belykh.

Additional information

The paper was recommended for publication by the Program Committee of the 7th International Scientific Conference “Mathematical Modeling, Optimization and Information Technologies (MMOTI-2021).”

Translated from Kibernetyka ta Systemnyi Analiz, No. 6, November–December, 2022, pp. 143–148.

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Belykh, T.V., Zorkaltsev, V.I. Interior-Point Algorithms: Creation History, Research Results, Applications, and Prospects*. Cybern Syst Anal 58, 977–982 (2022). https://doi.org/10.1007/s10559-023-00532-y

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  • DOI: https://doi.org/10.1007/s10559-023-00532-y

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