On Some Variational Problems Occurring in the Theory of Dynamic Programming
Richard Bellman, Irving Glicksberg, Oliver Gross · Proceedings of the National Academy of Sciences · 1953
Abstract : This paper presents some results of an investigation of a class of interesting and important variational problems involving the control of a physical system over a time interval. One large category of problems of this nature arises in connection with the maintenance of a dynamic system in or near a specified state at minimum cost. Another large category of problems, of economic and industrial origin, are those in which it is required to maximize the output of a system given a limited quantity of resources. Only one representative of this category will be discussed in this paper.