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Uspekhi Mat. Nauk, 1971, Volume 26, Issue 3(159), Pages 53–104 (Mi umn5198)  

This article is cited in 3 scientific papers (total in 3 papers)

On the theory of non-linear minimax problems

V. F. Dem'yanov, V. N. Malozemov


Abstract: This article is a survey of recent results on non-linear minimax problems. The following questions are considered: the directional differentiability of the maximum function; necessary conditions for a minimax and their geometrical interpretation; sufficient conditions for a local minimax; methods of successive approximation to find the stationary points of the maximum function; properties of the maximin function.
These questions are set out first of all for the discrete case (Ch. I) and then for the general case (Ch. II); in the first chapter the accent is on methods of successive approximation, while in the second it is on the tie-up between the theory, as it has evolved, and certain classical results.

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English version:
Russian Mathematical Surveys, 1971, 26:3, 57–115

Bibliographic databases:

UDC: 517.948+519.9
MSC: 90C47, 90C25, 90C30, 49M37, 41A50
Received: 16.01.1970

Citation: V. F. Dem'yanov, V. N. Malozemov, “On the theory of non-linear minimax problems”, Uspekhi Mat. Nauk, 26:3(159) (1971), 53–104; Russian Math. Surveys, 26:3 (1971), 57–115

Citation in format AMSBIB
\Bibitem{DemMal71}
\by V.~F.~Dem'yanov, V.~N.~Malozemov
\paper On the theory of non-linear minimax problems
\jour Uspekhi Mat. Nauk
\yr 1971
\vol 26
\issue 3(159)
\pages 53--104
\mathnet{http://mi.mathnet.ru/umn5198}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=297378}
\zmath{https://zbmath.org/?q=an:0216.42501}
\transl
\jour Russian Math. Surveys
\yr 1971
\vol 26
\issue 3
\pages 57--115
\crossref{https://doi.org/10.1070/RM1971v026n03ABEH003834}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Reuven Chen, “Solution of minimax problems using equivalent differentiable functions”, Computers & Mathematics with Applications, 11:12 (1985), 1165  crossref
    2. Cristina Gígola, Susana Gomez, “A Regularization Method for Solving the Finite Convex Min-Max Problem”, SIAM J Numer Anal, 27:6 (1990), 1621  crossref  mathscinet  zmath  isi
    3. A. V. Kolosnitsyn, “Computational efficiency of the simplex embedding method in convex nondifferentiable optimization”, Comput. Math. Math. Phys., 58:2 (2018), 215–222  mathnet  crossref  crossref  isi  elib
  • Успехи математических наук Russian Mathematical Surveys
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