Regularized Extragradient Method of Finding a Solution to an Optimal Control Problem with Inaccurately Specified Input Data

We consider an optimal control problem described by a system of linear ordinary differential equations with boundary conditions of general form defined by inequality-type constraints in the case when the input data are inaccurately specified. In general, such problems are unstable with respect to perturbations of the input data and require the development of special stable solution methods. In this paper we propose a regularized variant of the extragradient method, study its convergence, and construct a regularizing operator.