| Abstract: | In the first part of the paper, the equivalence of Lipschitzian differentiability of a function and a set of conditions of
weak convexity and weak concavity of this function is proved, as well as sufficient conditions for the continuous dependence
of the saddle point on a strongly convex-concave function of a parameter are given. In the second part, it is proved that
the value function of a game is smooth and the optimal positional and programmed strategies of the players are continuous
in zero-sum nonlinear differential games with strongly convex-concave Lagrangian.
Translated fromMatematicheskie Zametki, Vol. 66, No. 6, pp. 816–839 December, 1999. |
