  The article is devoted to the development of algorithmic methods ensuring
efficient complexity bounds for strongly convex-concave saddle point problems
in the case when one of the groups of variables is high-dimensional, and the
other is relatively low-dimensional (up to a hundred). The proposed technique
is based on reducing problems of this type to a problem of minimizing a convex
(maximizing a concave) functional in one of the variables, for which it is
possible to find an approximate gradient at an arbitrary point with the
required accuracy using an auxiliary optimization subproblem with another
variable. In this case, the ellipsoid method is used for low-dimensional
problems (if necessary, with an inexact $\delta$-subgradient), and accelerated
gradient methods are used for high-dimensional problems. For the case of a very
small dimension of one of the groups of variables (up to 5), an approach based
on a new version of the multidimensional analog of the Yu. E. Nesterov's method
on the square (multidimensional dichotomy) is proposed with the possibility of
using inexact values of the gradient of the objective functional.
