DYNAMIC PROGRAMMING TECHNIQUES.

The gneral theory of the recursive formulation of optimization problems is developed in this report. The conditions under which the problem of minimizing a functional over an abstract set which can be given a recursive formulation are analysed the distinction between deterministic and nondeterministic programming problems is included. The degree of state dependence of the criterion functional and the degree of Markovian character of the stochastic process generating system trajectories are analyzed for their effect on the recursive formulation. The recursive solution of the problem of finding the minimum value of a functional defined on a collection of curves is considered and the conditions under which the differential relation may be rigorously established are developed. A careful, heuristic, derivation of the Pontryagin Maximum Principle from this differential relation is also given. Problems discussed include the optimum scheduling of link-to-satellite assignments in a nonsynchronous satellite communication system and the computation of optimum discrete allocations. Author