A dual maximum principle for discrete-time linear systems with economic applications

A discrete-time linear optimal control problem with given initial and terminal times, state control constraints, and variable end points is set forth. Corresponding to this primal control problem, or maximization problem, is a dual linear control problem, or minimization problem. A dual maximum principle is proved with the aid of the duality theory of linear programming, where the dual of the Hamiltonian of the primal control problem is the Hamiltonian of the dual control problem. A discrete-time analog of the Hamilton-Jacobi equation is derived; and economic applications are discussed.