Solving multistage decision problems with non-separable performance indices via successive approximation

The authors present a successive approximation algorithm for solving a class of deterministic multistage decision problems with general performance indices, which cover both separable and non separable objective functions. Convergence of the algorithm is proved under certain conditions. The constraint qualification for the problems considered is also discussed. Since only a trajectory is needed to be stored in each iteration, the method can be used to solve some high-dimensional dynamic programming problems. The algorithm implementation and numerical results are presented, and future research is discussed