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Theory and Software Implementations of Shor’s r-Algorithms*

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Abstract

Three computational forms of r-algorithms with different amount of computation per iteration are considered. The results on the convergence of the limit variant of r-algorithms for convex smooth functions and the r μ (α)-algorithm for convex piecewise smooth functions are presented. Practical aspects of the variant of r (α)-algorithms with a constant coefficient of space dilation α and an adaptive method for step adjustment in the direction of the normalized anti-subgradient in the transformed space of variables are discussed.

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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

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  1. P. I. Stetsyuk
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Correspondence to P. I. Stetsyuk.

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*The study was financially supported by the NAS of Ukraine (Projects No. 0117U000327, No. 0116U004558) and Volkswagen Foundation (Grant # 90306).

Translated from Kibernetika i Sistemnyi Analiz, No. 5, September–October, 2017, pp. 43–57.

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Stetsyuk, P.I. Theory and Software Implementations of Shor’s r-Algorithms* . Cybern Syst Anal 53, 692–703 (2017). https://doi.org/10.1007/s10559-017-9971-1

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  • DOI: https://doi.org/10.1007/s10559-017-9971-1

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