A perturbation method for the numerical solution of optimization problems subject to inequality constraints explicitly containing the control is introduced. The effective ness of the computational algorithm is tested on the problem of optimizing the two-dimensional motion of a lifting re-entry vehicle, where the control variable (lift coefficient) is subject to an inequality constraint. Two iteration philosophies for correcting errors in the boundary conditions are suggested. With errors in the unknown boundary values in excess of 100%, the procedure converged to a terminal error norm of 4·15 × 10−11in 11 iterations using the more rapidly convergent iteration procedure.