An elimination condition to check the validity of the principle of optimality

In this paper, a simple elimination condition is introduced that may help in the verification or falsification of the principle of optimality and in deriving rigorously dynamic programming algorithms. Through two examples of single objective optimization, it is shown how the elimination condition can be used to rigorously derive dynamic programming schemes. The multiobjective optimization case, where the elimination approach was developed earlier, it is then briefly reviewed. Throughout two examples of game theory, it is demonstrated how the elmination condition is a necessary condition for the principle of optimality to hold. In these game examples, the elimination condition and the principle of optimality do not hold.