SYSTEMATIC and rapid steepest-ascent numerical procedure is described for determining optimum programs for nonlinear systems with terminal constraints. The procedure uses the concept of local linearization around a nominal (nonoptimum) path. The effect on the terminal conditions of a small change in the control variable program is determined by numerical integration of the adjoint differential equations for small perturbations about the nominal path. Having these adjoint (or influence) functions, it is then possible to determine the change in the control variable program that gives maximum increase in the pay-off function for a given mean-square perturbation of the control variable program while simultaneously changing the terminal quantities by desired amounts. By repeating this process in small steps, a control variable program that minimizes one quantity and yields specified values of other terminal quantities can be approached as closely as desired. Three numerical examples are presented: (a) The angle-of-attack program for a typical supersonic interceptor to climb to altitude in minimum time is determined with and without specified terminal velocity and heading. (6) The angle-of-attack program for the same interceptor to climb to maximum altitude is determined, (c) The angle-of-attack program is determined for a hypersonic orbital glider to obtain maximum surface range starting from satellite speed at 300,000 ft altitude.