In this paper, based on the Hamiltonian, an alternative interpretation about the iterative adaptive dynamic programming (ADP) approach from the perspective of optimization is developed for discrete time nonlinear dynamic systems. The role of the Hamiltonian in iterative ADP is explained. The resulting Hamiltonian driven ADP is able to evaluate the performance with respect to arbitrary admissible policies, compare two different admissible policies and further improve the given admissible policy. The convergence of the Hamiltonian ADP to the optimal policy is proven. Implementation of the Hamiltonian-driven ADP by neural networks is discussed based on the assumption that each iterative policy and value function can be updated exactly. Finally, a simulation is conducted to verify the effectiveness of the presented Hamiltonian-driven ADP.