Regularized extragradient method for finding a saddle point in an optimal control problem

We propose a regularized variant of the extragradient method of saddle point search for a convex-concave functional defined on solutions of control systems of linear ordinary differential equations. We assume that the input data of the problem are given inaccurately. Since the problem under consideration is, generally speaking, unstable under a disturbance in the input data, we propose a regularized variant of the extragradient method, investigate its convergence, and construct a regularizing operator. The regularization parameters of the method agree asymptotically with the disturbance level of the input data.