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: 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.
- Richard Bellman, Dynamic programming, Princeton University Press, Princeton, N. J., 1957. MR 0090477
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
- Richard Bellman, Dynamic programming and the smoothing problem, Management Sci. 3 (1956), 111–113. MR 81818, DOI https://doi.org/10.1287/mnsc.3.1.111
R. Bellman, Notes on the theory of control processes—I: On the minimum of maximum deviation, Quart. Appl. Math. XIV, 419–423 (1957)
- Richard Bellman, On a dynamic programming approach to the caterer problem. I, Management Sci. 3 (1957), 270–278. MR 91222, DOI https://doi.org/10.1287/mnsc.3.3.270
- Richard Bellman, Stability theory of differential equations, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1953. MR 0061235
- Richard Bellman, A survey of the mathematical theory of time-lag, retarded control, and hereditary processes, The Rand Corporation, Santa Monica, Calif., 1954. With the assistance of John M. Danskin, Jr. MR 0062327
- Richard Bellman, Dynamic programming and Lagrange multipliers, Proc. Nat. Acad. Sci. U.S.A. 42 (1956), 767–769. MR 82423, DOI https://doi.org/10.1073/pnas.42.10.767
- Richard Bellman, Irving Glicksberg, and Oliver Gross, On some variational problems occuring in the theory of dynamic programming, Rend. Circ. Mat. Palermo (2) 3 (1954), 363–397 (1955). MR 70076, DOI https://doi.org/10.1007/BF02849266
- R. Bellman, W. H. Fleming, and D. V. Widder, Variational problems with constraints, Ann. Mat. Pura Appl. (4) 41 (1956), 301–323. MR 79217, DOI https://doi.org/10.1007/BF02411673
S. Dreyfus, Dynamic programming solution of allocation problems, Techniques of Industrial Operations Research Seminar, Illinois Institute of Technology, June 1956
H. Osborn, Euler equations and characteristics, Chap. 7 of Dynamic programming of continuous processes, The RAND Corp., Rept. R-271, 1955
R. Bellman, Dynamic programming, Princeton University Press, 1957
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
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
R. Bellman, Notes on the theory of control processes—I: On the minimum of maximum deviation, Quart. Appl. Math. XIV, 419–423 (1957)
R. Bellman, On a dynamic programming approach to the caterer problem—I, Management Sci. 3, 270–278 (1957)
R. Bellman, Stability theory of differential equations, McGraw-Hill, 1953
R. Bellman, A survey of the mathematical theory of time-lag, retarded control, and hereditary processes, The RAND Corp. Rept. R-256, 1954
R. Bellman, Dynamic programming and Lagrange multipliers, Proc. Natl. Acad. Sci. 42, 767–769, (1956)
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)
R. Bellman, W. H. Fleming, and D. V. Widder, Variational problems with constraints, Annali di Matematica, Serie IV, Tomo XLI, 301–323, 1956
S. Dreyfus, Dynamic programming solution of allocation problems, Techniques of Industrial Operations Research Seminar, Illinois Institute of Technology, June 1956
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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Article copyright:
© Copyright 1958
American Mathematical Society
