Comparison of several numerical optimization methods

Several numerical methods for solving the nonlinear two-point boundary value problem associated with an optimum spacecraft trajectory are considered. A comparative evaluation of the methods is made to determine the relative merits of each method. Particular attention is given to such characteristics as the simplicity of formulation and implementation, the convergence sensitivity, the computing time required, and the computer storage requirements. The methods considered are the perturbation method, the quasilinearization method, and the gradient method. The numerical comparison is made by considering a two-dimensional, low-thrust, minimum-time, Earth-Mars trajectory.The authors are greatly indebted to Mr. Robert D. Witty, Lockheed Electronics Company, for providing the excellent programming support.