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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2018, Volume 58, Number 5, Pages 843–851
DOI: https://doi.org/10.7868/S0044466918050137
(Mi zvmmf10741)
 

This article is cited in 1 scientific paper (total in 1 paper)

Octahedral projections of a point onto a polyhedron

V. I. Zorkal'tsev

Energy Systems Institute, Siberian Branch, Russian Academy of Sciences, Irkutsk, Russia
Citations (1)
References:
Abstract: In computational methods and mathematical modeling, it is often required to find vectors of a linear manifold or a polyhedron that are closest to a given point. The “closeness” can be understood in different ways. In particular, the distances generated by octahedral, Euclidean, and Hölder norms can be used. In these norms, weight coefficients can also be introduced and varied. This paper presents the results on the properties of a set of octahedral projections of the origin of coordinates onto a polyhedron. In particular, it is established that any Euclidean and Hölder projection can be obtained as an octahedral projection due to the choice of weights in the octahedral norm. It is proven that the set of octahedral projections of the origin of coordinates onto a polyhedron coincides with the set of Pareto-optimal solutions of the multicriterion problem of minimizing the absolute values of all components.
Key words: linear inequalities, polyhedron, octahedral projections, Euclidean projections, Pareto-optimal solutions.
Funding agency Grant number
Russian Foundation for Basic Research 15-07-07412_а
Received: 25.05.2017
English version:
Computational Mathematics and Mathematical Physics, 2018, Volume 58, Issue 5, Pages 813–821
DOI: https://doi.org/10.1134/S0965542518050160
Bibliographic databases:
Document Type: Article
UDC: 519.72
Language: Russian
Citation: V. I. Zorkal'tsev, “Octahedral projections of a point onto a polyhedron”, Zh. Vychisl. Mat. Mat. Fiz., 58:5 (2018), 843–851; Comput. Math. Math. Phys., 58:5 (2018), 813–821
Citation in format AMSBIB
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\paper Octahedral projections of a point onto a polyhedron
\jour Zh. Vychisl. Mat. Mat. Fiz.
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\vol 58
\issue 5
\pages 843--851
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\crossref{https://doi.org/10.7868/S0044466918050137}
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\jour Comput. Math. Math. Phys.
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\pages 813--821
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  • https://www.mathnet.ru/eng/zvmmf/v58/i5/p843
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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    Abstract page:168
    References:31
     
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