The problem of minimizing the total pressure loss accompanying the breakdown of a supersonic flow to subsonic velocities through a system of successively ordered shock waves is considered. By changing to the corresponding problem of non-linear programming with non-linear constraints in the form of inequalities, a point which is suspected of being an extremum is determined and it is proved that it is the point of a strict local minimum. It is noted that, when the number of shock waves increases to infinity, the optimal shock wave system changes into an isoentropic wave.