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Sibirskii Matematicheskii Zhurnal, 2009, Volume 50, Number 5, Pages 1123–1136 (Mi smj2035)  

This article is cited in 5 scientific papers (total in 5 papers)

Multiobjective problems of convex geometry

S. S. Kutateladze

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Full-text PDF (364 kB) Citations (5)
References:
Abstract: Under study is the new class of geometrical extremal problems in which it is required to achieve the best result in the presence of conflicting goals; e.g., given the surface area of a convex body $\mathfrak x$, we try to maximize the volume of $\mathfrak x$ and minimize the width of $\mathfrak x$ simultaneously. These problems are addressed along the lines of multiple criteria decision making. We describe the Pareto-optimal solutions of isoperimetric-type vector optimization problems on using the techniques of the space of convex sets, linear majorization, and mixed volumes.
Keywords: isoperimetric problem, vector optimization, Pareto optimum, mixed volume, Alexandrov measure, linear majorization, Urysohn problem, Leidenfrost effect.
Received: 29.01.2009
English version:
Siberian Mathematical Journal, 2009, Volume 50, Issue 5, Pages 887–897
DOI: https://doi.org/10.1007/s11202-009-0099-z
Bibliographic databases:
UDC: 514.172+517.982+519.81+519.855
Language: Russian
Citation: S. S. Kutateladze, “Multiobjective problems of convex geometry”, Sibirsk. Mat. Zh., 50:5 (2009), 1123–1136; Siberian Math. J., 50:5 (2009), 887–897
Citation in format AMSBIB
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\paper Multiobjective problems of convex geometry
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\pages 1123--1136
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\pages 887--897
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  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский математический журнал Siberian Mathematical Journal
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    Abstract page:552
    Full-text PDF :171
    References:88
    First page:7
     
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