Dynamic programming: A global approach to determining necessary and sufficient conditions of optimality

We show how a weak version of the control problem may be reformulated as a convex programming problem. It is shown that there exists no duality gap associated with the convex programming problem and its dual. This property may be interpreted as a necessary and sufficient condition of optimality, akin to a well-known "verification" theorem formulated in terms of the Bellman equation. In contrast to previous results, the new conditions retain generality but involve no a priori assumptions concerning smoothness of the value function, existence of a regular synthesis, etc.