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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2020, Volume 492, Pages 104–107
DOI: https://doi.org/10.31857/S268695432003011X (Mi danma83) 		 
This article is cited in 2 scientific papers (total in 2 papers)

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Minimax-maximin relations for the problem of vector-valued criteria optimization

Yu. A. Komarov, A. B. Kurzhanskii

Lomonosov Moscow State University, Moscow, Russian Federation
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DOI: https://doi.org/10.31857/S268695432003011X
Abstract: The minimax-maximin relations for vector-valued functionals over the real field are studied. An increase in the dimensionality of criteria may result in a violation of some basic relations, for example, in an inequality between maximin and minimax that is always true for classic problems. Accordingly, the conditions for its correctness or violation need to be established. This paper introduces the definitions of set-valued minimax and maximin for multidimensional criteria and with an analogue in the classic minimax inequality. Necessary and sufficient conditions for its correctness and violation are described for two particular types of vector-valued functionals: the bilinear ones and those with separated variables.
Keywords: set-valued minimax, dynamic programming, multiobjective optimization, optimal control, Pareto frontier.
Funding agency Grant number
Russian Foundation for Basic Research 16–29–04191 офи_м
19–01–00613а
This work was supported by the Russian Foundation for Basic Research, project nos. 16-29-04191 ofi_m and 19-01-00613a.
Received: 25.12.2019
Revised: 06.04.2020
Accepted: 06.04.2020
English version:
Doklady Mathematics, 2020, Volume 101, Issue 3, Pages 259–261
DOI: https://doi.org/10.1134/S1064562420030114
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: Yu. A. Komarov, A. B. Kurzhanskii, “Minimax-maximin relations for the problem of vector-valued criteria optimization”, Dokl. RAN. Math. Inf. Proc. Upr., 492 (2020), 104–107; Dokl. Math., 101:3 (2020), 259–261
Citation in format AMSBIB
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\by Yu.~A.~Komarov, A.~B.~Kurzhanskii
\paper Minimax-maximin relations for the problem of vector-valued criteria optimization
\jour Dokl. RAN. Math. Inf. Proc. Upr.
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\vol 492
\pages 104--107
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\crossref{https://doi.org/10.31857/S268695432003011X}
\zmath{https://zbmath.org/?q=an:1476.49012}
\elib{https://elibrary.ru/item.asp?id=42930043}
\transl
\jour Dokl. Math.
\yr 2020
\vol 101
\issue 3
\pages 259--261
\crossref{https://doi.org/10.1134/S1064562420030114}
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