Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Some new techniques in the dynamic programming solution of variational problems

Author: Richard Bellman
Journal: Quart. Appl. Math. 16 (1958), 295-305
MSC: Primary 49.00; Secondary 65.00
DOI: https://doi.org/10.1090/qam/102032
MathSciNet review: 102032
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Abstract | References | Similar Articles | Additional Information

Abstract: In previous papers, it has been shown that the functional equation technique of dynamic programming may be applied to yield the numerical solution of a wide class of variational problems of the type occurring in mathematical physics, engineering, and economics.

References [Enhancements On Off] (What's this?)

  • [1] R. Bellman, Dynamic programming, Princeton University Press, 1957 MR 0090477
  • [2] R. Bellman, Dynamic programming and its application to variational problems in mathematical economics, Proceedings Symposium on Calculus of Variations and its Applications, Am. Math. Soc., 1955
  • [3] R. Bellman, On the application of the theory of dynamic programming to the study of control processes, Symposium on Non-linear circuit analysis, Polytechnic Institute of Brooklyn, vol. VI, 1956 MR 0081818
  • [4] R. Bellman, Notes on the theory of control processes--I: On the minimum of maximum deviation, Quart. Appl. Math. XIV, 419-423 (1957)
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  • [7] R. Bellman, A survey of the mathematical theory of time-lag, retarded control, and hereditary processes, The RAND Corp. Rept. R-256, 1954 MR 0062327
  • [8] R. Bellman, Dynamic programming and Lagrange multipliers, Proc. Natl. Acad. Sci. 42, 767-769, (1956) MR 0082423
  • [9] R. Bellman, I. Glicksberg and O. Gross, On some variational problems occurring in the theory of dynamic programming, Rendiconti del Circolo Matematico di Palermo, Serie II, Tomo III 1-35 (1954) MR 0070076
  • [10] R. Bellman, W. H. Fleming, and D. V. Widder, Variational problems with constraints, Annali di Matematica, Serie IV, Tomo XLI, 301-323, 1956 MR 0079217
  • [11] S. Dreyfus, Dynamic programming solution of allocation problems, Techniques of Industrial Operations Research Seminar, Illinois Institute of Technology, June 1956
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Additional Information

DOI: https://doi.org/10.1090/qam/102032
Article copyright: © Copyright 1958 American Mathematical Society

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