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Diskr. Mat., 2011, Volume 23, Issue 3, Pages 82–92 (Mi dm1154)  

This article is cited in 3 scientific papers (total in 3 papers)

On stability of the gradient algorithm in convex discrete optimisation problems and related questions

A. B. Ramazanov


Abstract: We introduce the notion of steepness of a coordinate-convex function of discrete argument on an ordinal-convex set. In terms of guaranteed estimates it is shown that in problems of optimisation of coordinate-convex functions on an ordinal-convex set the gradient coordinatewise lifting algorithm is stable under small perturbations of the utility function. As corollaries we obtain improved guaranteed estimates for accuracy of the gradient algorithm, and also new sufficient conditions for the values of the utility function of the problem under consideration to coincide in the global and gradient extrema.

DOI: https://doi.org/10.4213/dm1154

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English version:
Discrete Mathematics and Applications, 2011, 21:4, 465–476

Bibliographic databases:

UDC: 519.10
Received: 09.07.2009

Citation: A. B. Ramazanov, “On stability of the gradient algorithm in convex discrete optimisation problems and related questions”, Diskr. Mat., 23:3 (2011), 82–92; Discrete Math. Appl., 21:4 (2011), 465–476

Citation in format AMSBIB
\Bibitem{Ram11}
\by A.~B.~Ramazanov
\paper On stability of the gradient algorithm in convex discrete optimisation problems and related questions
\jour Diskr. Mat.
\yr 2011
\vol 23
\issue 3
\pages 82--92
\mathnet{http://mi.mathnet.ru/dm1154}
\crossref{https://doi.org/10.4213/dm1154}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2895516}
\elib{http://elibrary.ru/item.asp?id=20730397}
\transl
\jour Discrete Math. Appl.
\yr 2011
\vol 21
\issue 4
\pages 465--476
\crossref{https://doi.org/10.1515/DMA.2011.029}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-81555210190}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Emelichev V.A., Ramazanov A.B., “About the Steepness of the Function of Discrete Argument”, TWMS J. Pure Appl. Math., 7:1 (2016), 105–111  mathscinet  isi
    2. Ramazanov A.B., “New of Accuracy of Gradient Algorithm in the Jordan-Dedekinds Structure”, Appl. Comput. Math., 17:1 (2018), 109–113  mathscinet  isi
    3. Ramazanov A.B., “On Stability of the Gradient Algorithm For One Separable Nonlinear Discrete Optimization Problems”, Proceedings of the 6Th International Conference on Control and Optimization With Industrial Applications, Vol i, eds. Fikret A., Tamer B., Baku State Univ, Inst Applied Mathematics, 2018, 312–314  isi
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