Invariant Imbedding and a Class of Variational Problems.

by J. L. Casti, Robert E. Kalaba, B. J. Vereeke


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Many problems in physics, technology, biology, and operations research lead to the minimization of a functional, and typically the minimizer is characterized as the solution of an Euler equation, together with certain boundary conditions. One aim of the theory of invariant imbedding is to convert these boundary value problems into initial-value problems which have certain computational advantages. This study shows that for a class of minimization problems, the invariant imbedding equations can be obtained directly from the variational problem without making use of the Euler equation or Bellman's principle of optimality. It then shows that the solution of the initial-value problem satisfies the Euler equation. 18 pp. Refs.

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