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.
\Bibitem{DemMal71}
\by V.~F.~Dem'yanov, V.~N.~Malozemov
\paper On the theory of non-linear minimax problems
\jour Russian Math. Surveys
\yr 1971
\vol 26
\issue 3
\pages 57--115
\mathnet{http://mi.mathnet.ru/eng/rm5198}
\crossref{https://doi.org/10.1070/RM1971v026n03ABEH003834}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=297378}
\zmath{https://zbmath.org/?q=an:0216.42501}
Linking options:
https://www.mathnet.ru/eng/rm5198
https://doi.org/10.1070/RM1971v026n03ABEH003834
https://www.mathnet.ru/eng/rm/v26/i3/p53
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