Abstract
This paper discusses an optimal control theory-discrete maximum principle-for distributed-lag models. The system equation is described by a multidimensional nonlinear difference equation of high-order. A Hamiltonian for this model is newly defined in this paper, and the discrete maximum principle is shown in terms of this Hamiltonian. The discrete maximum principle is proved by the theory of mathematical programming (Kuhn-Tucker Theorem). An economic interpretation for the adjoint variables and the Hamiltonian is clearly shown. Finally, it is shown that the gradient vector of the objective function with respect to the control variables is equal to the gradient vector of the Hamiltonian with respect to the control variables.
