Introduction O PTIMAL control problems with bounded controls reduce to two-point boundary-value problems which are difficult to handle by conventional methods of calculus of variations. Pontryagin's maximum principle and Bellman's dynamic programming are the other methods for solving such problems. In this paper the optimal control problem is transformed into one of mathematical programming by a Raleigh-Ritz-type procedure. This is essentially a penalty function approach which penalizes the given performance index for not satisfying the differential constraints. The resulting mathematical programming problem is then solved by SWIFT—Sequential Weightage Increasing Factor Technique developed by the authors. The method is illustrated by obtaining the thrust angle history of a probe for an Earth-to-Mars orbit transfer in minimum time. Good comparison of the time obtained by this method with the actual time taken by the Viking-2 spacecraft is extremely interesting. Other methods' do not show such a good comparison.