Extremal problems with separable graphs

The property of separability of a graph was introduced for extremal problems with equality constraints; this generalizes the convexity property of the problem. The equality of the optimal values of the original problem and its dual problem appears as an analytic equivalent of this property; here the dual problem can be interpreted as a convex optimization problem on a space of generalized (randomized) arguments. The solution method based on N. N. Krasovskii's extremal shift principle can be justified on the basis of these relations for extremal problems with separable graphs; the method was illustrated by an example of optimal control problems.