THE DISCRETE MAXIMUM PRINCIPLE WITH APPLICATIONS TO MANAGEMENT SCIENCE.

Abstract : A general version of the discrete control system is formulated which includes difference inequalities and the possibility of inequality as well as equality state space constraints. The authors apply the well-known Kuhn-Tucker theorem to derive necessary conditions that the primal and adjoint functions must satisfy in order that they be a solution to the optimum control problem. These necessary conditions are valid only if the constraint qualification holds. One of the necessary conditions is the Pontryagin maximum principle. A special version of the general problem is stated, and applied to a separable non-linear programming problem. Finally, production control examples are solved by means of the theory. (Author)