On the algorithms of dynamic programming for optimal processes

The problem of discrete optimal control which has $m$ consistently applied objective functions is formulated. In this problem the optimal process, also called $m$-optimal, is sought as a pair of functions defined on a finite set of steps at the links by which one function is uniquely defines the other, with the constraints of these functions with inclusion "$\in$" of their values in the final multiple values of the functions of the known pair. A uniform representation of sets, forming the $k$-optimal processes for $k$ not greater than $m$, is given with construction of nondecreasing sequence, upper limited by this pair by the "$\subset $" inclusions, on the basis of characterization of solvability of the problem.