A combination of the classical Lagrange multiplier formalism and the functional equation technique of dynamic programming enables us to treat a number of types of variational problems involving the computation and tabulation of functions.
Bellman, Richard Ernest, Dynamic Programming and LaGrange Multipliers. Santa Monica, CA: RAND Corporation, 1956. https://www.rand.org/pubs/papers/P869.html. Also available in print form.
Bellman, Richard Ernest, Dynamic Programming and LaGrange Multipliers, Santa Monica, Calif.: RAND Corporation, P-869, 1956. As of October 06, 2021: https://www.rand.org/pubs/papers/P869.html