Geodesic
Saddle point for differential games with strongly convex-concave integrand
Matematičeskie zametki, Tome 62 (1997) no. 5, pp. 725-743 
G. E. Ivanov. Saddle point for differential games with strongly convex-concave integrand. Matematičeskie zametki, Tome 62 (1997) no. 5, pp. 725-743. http://geodesic.mathdoc.fr/item/MZM_1997_62_5_a9/
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     author = {G. E. Ivanov},
     title = {Saddle point for differential games with strongly convex-concave integrand},
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     year = {1997},
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     url = {http://geodesic.mathdoc.fr/item/MZM_1997_62_5_a9/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

On a fixed time interval we consider zero-sum nonlinear differential games for which the integrand in the criterion functional is a sufficiently strongly convex-concave function of chosen controls. It is shown that in our setting there exists a saddle point in the class of programmed strategies, and a minimax principle similar to Pontryagin's maximum principle is a necessary and sufficient condition for optimality. An example in which the class of games under study is compared with two known classes of differential games is given.

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