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Sbornik: Mathematics, 2011, Volume 202, Issue 5, Pages 697–719
DOI: https://doi.org/10.1070/SM2011v202n05ABEH004162 (Mi sm7621) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Optimal probabilistic search

L. V. Lokutsievskiy

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (393 kB) Citations (3)
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DOI: https://doi.org/10.1070/SM2011v202n05ABEH004162
Abstract: This paper is concerned with the optimal search of an object at rest with unknown exact position in the $n$-dimensional space. A necessary condition for optimality of a trajectory is obtained. An explicit form of a differential equation for an optimal trajectory is found while searching over $R$-strongly convex sets. An existence theorem is also established.
Bibliography: 8 titles.
Keywords: optimal search, probabilistic search, optimal trajectory, vortex singularity, existence of an optimal search trajectory.
Received: 13.08.2009 and 09.11.2010
Russian version:
Matematicheskii Sbornik, 2011, Volume 202, Number 5, Pages 77–100
DOI: https://doi.org/10.4213/sm7621
Bibliographic databases:
Document Type: Article
UDC: 517.977.5
MSC: 91A24, 49N70
Language: English
Original paper language: Russian
Citation: L. V. Lokutsievskiy, “Optimal probabilistic search”, Mat. Sb., 202:5 (2011), 77–100; Sb. Math., 202:5 (2011), 697–719
Citation in format AMSBIB
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  • https://doi.org/10.1070/SM2011v202n05ABEH004162
  • https://www.mathnet.ru/eng/sm/v202/i5/p77
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:691
    Russian version PDF:214
    English version PDF:12
    References:80
    First page:25
     
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