The cost function assigns a real number to any given plan in the execution space that we have chosen and satisfies the principle of optimality [Cormen et al.

Such an approach guarantees the optimal, since the optimization problem satisfies the principle of optimality, i.e., an optimal plan for a set of relations must be an extension of an optimal plan for some subset of the set.

Moreover, the principle of optimality is self-explanatory: it is for the best that everything should be for the best (p.

One worries, however, whether the principle of optimality is not in fact more ontologically obscure than the theistic explanation.

It is, rather, the

principle of optimality reflected in the second premise that is self-explanatory--the fact that the best possible order exists.

According to the

principle of optimality in dynamic programming, HJB equation for the savings-consumption problem (7) evolves as

(6) over the sequence of the forcing vector, the dynamic programming method and Bellman principle of optimality are applied.

The recurrence formula can be derived by applying the Bellman principle of optimality:

In the following theorem we give a simple, necessary, and sufficient condition for TSP adaptive stability based on Bellman's principle of optimality.

Platonov, "Measure of quasistabiiity of a vector integer linear programming problem with generalized principle of optimality in the Helder metric," Buletinul Academiei de Stiinte a Republicii Moldova: Matematica, vol.

Finally, in chapter 11, Nicholas Rescher, after explaining the difference between axiological explanation and efficient causality, defends the

principle of Optimality, "whatever possibility is for the best is ipso facto the possibility that is actualized," as the answer to two understandings of the ultimate why question.

The second principle under the indirect approach is the Hamilton Jacobi-Bellman (HJB) formulation that transforms the problem of optimizing the cost functional [PHI] in (2) into the resolution of a partial differential equation by utilizing the

principle of optimality in equation (11) (Bryson and Ho, 1975; Kirk, 1970).