Invariant Imbedding

Proceedings of the Summer Workshop on Invariant Imbedding held at the University of Southern California, June – August 1970

  • R. E. Bellman
  • E. D. Denman
Conference proceedings

Part of the Lecture Notes in Operations Research and Mathematical Systems book series (LNE, volume 52)

About these proceedings


Imbedding is a powerful and versatile tool for problem­ solving. Rather than treat a question in isolation, we view it as a member of a family of related problems. Each member then becomes a stepping stone in a path to a simultaneous solution of the entire set of problems. As might be expected, there are many ways of accomplishing this imbedding. Time and space variables have been widely employed in the past, while modern approaches combine these structural features with others less immediate. Why should one search for alternate imbeddings when elegant classical formalisms already exist? There are many reasons. To begin with, different imbeddings are useful for different purposes. Some are well suited to the derivation of existence and uniqueness theorems, some to the derivation of conservation relations, some to perturbation techniques and sensitivity analysis, some to computa­ tional studies. The digital computer is designed for initial value problems; the analog computer for boundary-value problems. It is essential then to be flexible and possess the ability to use one device or the other, or both. In economics, engineering, biology and physics, some pro­ cesses lend themselves more easily to one type of imbedding rather than another. Thus, for example, stochastic decision processes are well adapted to dynamic programming. In any case, to go hunting in the wilds of the scientific world armed with only one arrow in one's quiver is quite foolhardy.


Stochastic Decision Processes differential equation dynamic programming economics optimal control

Editors and affiliations

  • R. E. Bellman
    • 1
  • E. D. Denman
    • 2
  1. 1.University of Southern CaliforniaLos AngelesUSA
  2. 2.University of HoustonHoustonUSA

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1971
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-05549-5
  • Online ISBN 978-3-642-46274-0
  • Series Print ISSN 0075-8442
  • Buy this book on publisher's site
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