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The Generalized Ellipsoid Method*

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Abstract

An algorithm with space dilation is presented, which is the circumscribed ellipsoid method under a certain choice of dilation coefficient. It is shown that its special case is the Yudin–Nemirovsky–Shor ellipsoid method. The application of the algorithm to solving a convex programming problem and the problem of finding a saddle point of a convex-concave function are described.

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Authors and Affiliations

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

    P. I. Stetsyuk, O. V. Fesiuk & O. N. Khomyak

Authors
  1. P. I. Stetsyuk
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  2. O. V. Fesiuk
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  3. O. N. Khomyak
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Corresponding author

Correspondence to P. I. Stetsyuk.

Additional information

*The study was supported by the National Academy of Sciences of Ukraine (projects No. 0117U000327, No. 0116U004558) and Volkswagen Foundation (grant No. 90 306).

Translated from Kibernetika i Sistemnyi Analiz, No. 4, July–August, 2018, pp. 70–80.

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Stetsyuk, P.I., Fesiuk, O.V. & Khomyak, O.N. The Generalized Ellipsoid Method*. Cybern Syst Anal 54, 576–584 (2018). https://doi.org/10.1007/s10559-018-0058-4

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  • DOI: https://doi.org/10.1007/s10559-018-0058-4

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