A numerical method of solving a linear problem on a minimum consumption of resources

A simple algorithm of developing a quasi-optimal control relative to the consumption of resources is considered. The control is used as an initial approach to an iterative procedure of computing the optimal control. A system of linear algebraic equations is obtained that approximately relays the increments of the initial conditions of the adjoint system to the increments of the amplitudes of the quasi-optimal control over ultimate values. A local convergence of the computing process with a quadratic rate is proved, a radius of the local convergence being found. The condition of global convergence of the method is determined.