guidance, flight mechanics and trajectory optimization

The optimum path can be found by starting at city A and following the arrows
from left to right. This path is shown by a heavy line in the sketch.
There is an advantage to each of these computational procedures depending
upon the nature of the problem. In some problems, the terminal constraints
are of such a nature that it is computationally advantageous to start computing
at the end of the problem and progress to the beginning. In other problems,
the reverse may be true. The preceding sample problem was equally suitable
to either method. Depending upon the formulation of the problem, the costs
for typical transitions may not be unique (the cost could depend upon the
path as in trajectory problems) as they were in the sample problem. This
may be a factor that will influence the choice of the method to be used.
To summarize, the optimal value function and the Principle of Optimality
have been used to determine the best decision policy for the multi-stage
decision process: the optimal value function kept track of at least expensive
possible cost for each city while the Principle of Optimality used this
optimum cost as a means by which it could make a decision for the next
stage of the process. Then, a new value for the optimal value function was
computed for the next stage. After the computation was complete, each stage
had a corresponding decision that was made and which was used to determine
the optimum path.
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