ИСТИНА

The optimal control problem with free right end and linear differential equations constraints is considered. The right-hand ends of controls and trajectories generate a finite-dimensional Cartesian product, on which a minimum of the objective function is defined under constraints such as input-output model of Leontief. To solve this problem we suggest an iterative method of extra-proximal type, consisting in the construction of the functional sequences of trajectories and controls. It was proved that the sequences of controls, trajectories, conjugate trajectories, as well as the sequences in finite-dimensional spaces of primal and dual variables converge monotonically in norm to solution of the problem.