Dynamic Programming and the Calculus of Variations

A demonstration of the relationships between the calculus of variations, a mathematical discipline concerning certain problems of optimization theory, and dynamic programming, a newer mathematical approach applicable to optimization problems. In addition to explaining and contrasting the two approaches, the Report shows that many results of the calculus of variations become simple and intuitively apparent when examined from the dynamic programming viewpoint. In emphasizing the geometrical and physical insight afforded by this approach, the study shows how these techniques can be applied, for instance to stochastic and adaptive variational problems. It can be used in the study of dynamic programming and other new mathematical formalisms; in optimal control problems, such as the determination of rocket trajectories, the correction of launch errors and inflight disturbances of spacecraft; and in the problems of optimal control found in economics, biology, and the social sciences.