Geodesic
On the theory of non-linear minimax problems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 26 (1971) no. 3, pp. 57-115

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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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V. F. Dem'yanov; V. N. Malozemov. On the theory of non-linear minimax problems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 26 (1971) no. 3, pp. 57-115. http://geodesic.mathdoc.fr/item/RM_1971_26_3_a1/