Geodesic
On the algorithms of dynamic programming for optimal processes
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 3 (2012), pp. 215-218

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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.
Keywords: discrete optimal control, consistently applied criteria, dynamic programming, algorithms. 
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     author = {V. G. Ovchinnikov},
     title = {On the algorithms of dynamic programming for optimal processes},
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     year = {2012},
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     url = {http://geodesic.mathdoc.fr/item/VSGTU_2012_3_a26/}
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V. G. Ovchinnikov. On the algorithms of dynamic programming for optimal processes. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 3 (2012), pp. 215-218. http://geodesic.mathdoc.fr/item/VSGTU_2012_3_a26/