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.
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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/

[1] Aizeks R., Differentsialnye igry, Mir, M., 1967

[2] Pontryagin L. S., “Lineinye differentsialnye igry presledovaniya”, Matem. sb., 112:3 (1980), 307–330 | MR | Zbl

[3] Krasovskii N. N., Upravlenie dinamicheskoi sistemoi, Nauka, M., 1985

[4] Rockafellar R. T., “Integral functionals, normal integrands and measurable selections”, Lecture Notes in Math., 543, 1976, 157–207 | MR | Zbl

[5] Ekland I., Temam R., Vypuklyi analiz i variatsionnye problemy, Mir, M., 1979

[6] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1989

[7] fon Neiman Dzh., “K teorii strategicheskikh igr”, Matrichnye igry, Fizmatgiz, M., 1961, 173–204