A problem to minimize total pressure losses is considered for the case, when a supersonic flow is decelerated to subsonic velocities in a system consisting of shock waves sequentially situated. A point being suspicious for extremum is determined as a result of the transition to a corresponding problem of nonlinear programming with nonlinear restrictions - inequalities. It is proved that this point is the point of strict local minimum. It is pointed out that, as the number of shock waves increases up to infinity, the optimal shock-wave system transforms into a isoentropic wave.