Solving strongly convex-concave composite saddle-point problems with low dimension of one group of variable

Algorithmic methods are developed that guarantee efficient complexity estimates for strongly convex-concave saddle-point problems in the case when one group of variables has a high dimension, while another rather low dimension (up to 100). These based on reducing this type minimization (maximization) problem convex (concave) functional with respect such an approximate value gradient at arbitrary point can be obtained required accuracy using auxiliary optimization subproblem other variable. It is proposed use ellipsoid method and Vaidya's low-dimensional accelerated inexact information about or subgradient high-dimensional problems. In variables, ranging over hypercube, very five), approach efficient. This new version multidimensional analogue Nesterov's square (the dichotomy method) possibility values objective functional. Bibliography: 28 titles.