Dynamic programming and the Jacobi condition of the calculus of variations

by Stuart E. Dreyfus

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An examination of the assumption that a discrete version of an optimization problem approaches the continuous statement as the increment in the independent variable approaches zero. A condition that must be satisfied if the passage to the limit is to be valid is discovered and shown to be equivalent to the Jacobi necessary condition of the classical theory. This exploration yields a new form of the Jacobi condition, which provides a rule for adjusting the optimal solution to take into account slightly perturbed initial conditions. 18 pp.

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