SOME NEW TECHNIQUES IN THE DYNAMIC PROGRAMMING SOLUTION OF VARIATIONAL PROBLEMS
Abstract : It was seen that the numerical solution of a problem involving N state variables depended upon the computation of sequences of functions of N variables. This fact made the method routine only for the case where N = 1 or 2, with grave difficulties arising in the general case. In the paper, it is indicated how to overcome this difficulty for a large class of problems in which the underlying equations and the criterion function are linear, although the restraints on the forcing functions may be nonlinear, corresponding say to energy considerations. Finally, it is briefly indicated how the method of successive approximations may be combined with the foregoing techniques to reduce general variational problems, in which the equations and criterion function are nonlinear, to sequences of problems which can be solved numerically by means of sequences of functions of one variable.