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.

**[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)**[5]**R. Bellman,*On a dynamic programming approach to the caterer problem--I*, Management Sci.**3**, 270-278 (1957) MR**0091222****[6]**R. Bellman,*Stability theory of differential equations*, McGraw-Hill, 1953 MR**0061235****[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**[12]**H. Osborn,*Euler equations and characteristics*, Chap. 7 of*Dynamic programming of continuous processes*, The RAND Corp., Rept. R-271, 1955

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Additional Information

DOI:
https://doi.org/10.1090/qam/102032

Article copyright:
© Copyright 1958
American Mathematical Society