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Matematicheskie Zametki, 1997, Volume 62, Issue 5, Pages 725–743
DOI: https://doi.org/10.4213/mzm1659 (Mi mzm1659) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Saddle point for differential games with strongly convex-concave integrand

G. E. Ivanov

Moscow Institute of Physics and Technology
Full-text PDF (1278 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm1659
Abstract: On a fixed time interval we consider zero-sum nonlinear differential games for which the integrand in the criterion functional is a sufficiently strongly convex-concave function of chosen controls. It is shown that in our setting there exists a saddle point in the class of programmed strategies, and a minimax principle similar to Pontryagin's maximum principle is a necessary and sufficient condition for optimality. An example in which the class of games under study is compared with two known classes of differential games is given.
Received: 07.02.1995
Revised: 02.07.1997
English version:
Mathematical Notes, 1997, Volume 62, Issue 5, Pages 607–622
DOI: https://doi.org/10.1007/BF02361299
Bibliographic databases:
UDC: 517.9
Language: Russian
Citation: G. E. Ivanov, “Saddle point for differential games with strongly convex-concave integrand”, Mat. Zametki, 62:5 (1997), 725–743; Math. Notes, 62:5 (1997), 607–622
Citation in format AMSBIB
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\by G.~E.~Ivanov
\paper Saddle point for differential games with strongly convex-concave integrand
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\yr 1997
\vol 62
\issue 5
\pages 725--743
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\zmath{https://zbmath.org/?q=an:0915.90286}
\transl
\jour Math. Notes
\yr 1997
\vol 62
\issue 5
\pages 607--622
\crossref{https://doi.org/10.1007/BF02361299}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000075396200010}
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  • https://www.mathnet.ru/eng/mzm1659
  • https://doi.org/10.4213/mzm1659
  • https://www.mathnet.ru/eng/mzm/v62/i5/p725
    • This publication is cited in the following 3 articles:
    1. Mikhail I. Krastanov, Rossen Rozenov, Boyan K. Stefanov, “On a Constrained Infinite-Time Horizon Linear Quadratic Game”, Dyn Games Appl, 13:3 (2023), 843  crossref
    2. Yegorov I., Grognard F., Mailleret L., Halkett F., Bernhard P., “A Dynamic Game Approach to Uninvadable Strategies For Biotrophic Pathogens”, Dyn. Games Appl., 10:1 (2020), 257–296  crossref  isi
    3. G. E. Ivanov, “Continuity of optimal controls in differential games, and some properties of weakly and strongly convex functions”, Math. Notes, 66:6 (1999), 675–693  mathnet  crossref  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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