Abstract: The paper proposes the discrete approximate iteration method to solve single-dimensional continuing dynamic programming model. At the same time, multidimensional continuing dynamic programming model is solved by the discrete approximate iteration method and bi-convergent method. The algorithm is as following: Firstly, let state value of one of state equations be unknown and the others be known. Secondly, use the discrete approximate iteration method to find the optimal value of the unknown state values and then continue iterating until all state equations have found optimal values. If the objective function is non-concave and non-convex, the convergence of the algorithm is proved. If the objective function is convex, the linear convergence of the algorithm is proved. At last, the effectiveness of the formation and the algorithm is proved by an example.

Key words:  dynamic programming, dimension, discrete approximate iteration, bi-convergent method