Extragradient method of optimal control with terminal constraints

For the case where the objective function is minimized over part of the set of attainability defined by a system of linear inequalities, consideration was given to a method of solving the optimal control problem over a fixed time interval with free right end and constraints in the form of a linear differential equation. An iterative extragradient process formulated in the functional subspace of the sectionally continuous controls from L 2 ^r was proposed, and its convergence was proved.