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Sibirskii Matematicheskii Zhurnal, 2009, Volume 50, Number 5, Pages 1123–1136
(Mi smj2035)
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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
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
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
Linking options:
https://www.mathnet.ru/eng/smj2035 https://www.mathnet.ru/eng/smj/v50/i5/p1123
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Abstract page: | 552 | Full-text PDF : | 171 | References: | 88 | First page: | 7 |
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