A dynamic programming scheme with multidimensional step indexing

The classical dynamic programming scheme with computation for one sequence of steps is generalized to the case of several indexed sequences in which the solution at every step depends on the results found at preceding steps of each of these sequences. The Bellman equations are generalized and proved, the complexity of algorithms is estimated, computer-aided realization is described, and applied problems whose formalization leads to a dynamic programming problem with multidimensional step indexing are stated.