Geodesic
Saddle point for differential games with strongly convex-concave integrand
Matematičeskie zametki, Tome 62 (1997) no. 5, pp. 725-743

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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. 
@article{MZM_1997_62_5_a9,
     author = {G. E. Ivanov},
     title = {Saddle point for differential games with strongly convex-concave integrand},
     journal = {Matemati\v{c}eskie zametki},
     pages = {725--743},
     publisher = {mathdoc},
     volume = {62},
     number = {5},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_62_5_a9/}
}
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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/