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Izvestiya: Mathematics, 2001, Volume 65, Issue 1, Pages 99–121
DOI: https://doi.org/10.1070/im2001v065n01ABEH000323 (Mi im323) 		 
This article is cited in 11 scientific papers (total in 11 papers)

The subdifferential and the directional derivatives of the maximum of a family of convex functions. II

V. N. Solov'ev

M. V. Lomonosov Moscow State University
English version PDF (646 kB) Citations (11)
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DOI: https://doi.org/10.1070/im2001v065n01ABEH000323
Abstract: The paper deals with calculating the directional derivatives and the subdifferential of the maximum of convex functions with no compactness conditions on the indexing set. We apply our results to the problems of minimax theory in which the Lagrange function is not assumed to be concave. We also apply these results to the duality theory of non-convex extremum problems, and strengthen earlier results of Yakubovich, Matveev and the author. We illustrate our results by investigating a problem of optimal design of experiments.
Received: 29.09.1999
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2001, Volume 65, Issue 1, Pages 107–132
DOI: https://doi.org/10.4213/im323
Bibliographic databases:
MSC: 49J52, 26B05, 26B25, 46G05, 26A51
Language: English
Original paper language: Russian
Citation: V. N. Solov'ev, “The subdifferential and the directional derivatives of the maximum of a family of convex functions. II”, Izv. RAN. Ser. Mat., 65:1 (2001), 107–132; Izv. Math., 65:1 (2001), 99–121
Citation in format AMSBIB
\Bibitem{Sol01}
\by V.~N.~Solov'ev
\paper The subdifferential and the directional derivatives of the maximum of a~family of convex functions.~II
\jour Izv. RAN. Ser. Mat.
\yr 2001
\vol 65
\issue 1
\pages 107--132
\mathnet{http://mi.mathnet.ru/im323}
\crossref{https://doi.org/10.4213/im323}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1829407}
\zmath{https://zbmath.org/?q=an:1017.49020}
\transl
\jour Izv. Math.
\yr 2001
\vol 65
\issue 1
\pages 99--121
\crossref{https://doi.org/10.1070/im2001v065n01ABEH000323}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33747103818}
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  • https://doi.org/10.1070/im2001v065n01ABEH000323
  • https://www.mathnet.ru/eng/im/v65/i1/p107
    Cycle of papers
    This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:706
    Russian version PDF:318
    English version PDF:38
    References:110
    First page:1
     
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