  The paper considers approaches to saddle point problems with a two-sided
variant of the Polyak-Lojasievich condition based on the gradient method with
inexact information and proposes a stopping rule based on the smallness of the
norm of the inexact gradient of the external subproblem. Achieving this rule in
combination with a suitable accuracy of solving the auxiliary subproblem
ensures that the quality of the original saddle point problem is acceptable.
The results of numerical experiments for various saddle point problems are
discussed to illustrate the effectiveness of the proposed method, including the
comparison with proven convergence rate estimates.
