Before revision:  In the first iteration, optimal solutions to the local problems are computed, from leaf nodes to the root node, in terms of the coupling variables. In the second iteration, in the reverse order, the local optimal solutions are instantiated with specific values of the coupling variables. Restricted to constant controls, the optimal solutions to the local problems possess a piecewise linear property, which facilitates analytical solution.
After revision:  When restricted to the class of one-shot control actions, the optimal solutions to the local problems possess a piecewise linear property, which facilitates analytical solution.