The theory of dynamic programming

Author:
Richard Bellman

Journal:
Bull. Amer. Math. Soc. **60** (1954), 503-515

DOI:
https://doi.org/10.1090/S0002-9904-1954-09848-8

MathSciNet review:
0067459

Full-text PDF Free Access

References | Additional Information

- K. J. Arrow, D. Blackwell, and M. A. Girshick,
*Bayes and minimax solutions of sequential decision problems*, Econometrica**17**(1949), 213–244. MR**32173**, DOI https://doi.org/10.2307/1905525
2. K. J. Arrow, T. E. Harris, and J. Marschak, Optimal inventory policy, Cowles Commission Paper No. 44, 1951.
- Richard Bellman,
*An introduction to the theory of dynamic programming*, The Rand Corporation, Santa Monica, Calif., 1953. MR**0061805** - Richard Bellman,
*On games involving bluffing*, Rend. Circ. Mat. Palermo (2)**1**(1952), 139–156. MR**53470**, DOI https://doi.org/10.1007/BF02847783 - Richard Bellman,
*On the theory of dynamic programming*, Proc. Nat. Acad. Sci. U.S.A.**38**(1952), 716–719. MR**50856**, DOI https://doi.org/10.1073/pnas.38.8.716 - Richard Bellman,
*Some problems in the theory of dynamic programming*, Econometrica**22**(1954), 37–48. MR**60709**, DOI https://doi.org/10.2307/1909830 - Richard Bellman,
*Bottleneck problems and dynamic programming*, Proc. Nat. Acad. Sci. U.S.A.**39**(1953), 947–951. MR**61808**, DOI https://doi.org/10.1073/pnas.39.9.947 - Richard Bellman,
*An introduction to the theory of dynamic programming*, The Rand Corporation, Santa Monica, Calif., 1953. MR**0061805** - Richard Bellman,
*Some functional equations in the theory of dynamic programming*, Proc. Nat. Acad. Sci. U.S.A.**39**(1953), 1077–1082. MR**61806**, DOI https://doi.org/10.1073/pnas.39.10.1077 - Richard Bellman,
*Dynamic programming and a new formalism in the calculus of variations*, Proc. Nat. Acad. Sci. U.S.A.**40**(1954), 231–235. MR**61289**, DOI https://doi.org/10.1073/pnas.40.4.231
11. R. Bellman, The theory of dynamic programming, a general survey, Chapter from "Mathematics for Modern Engineers" by E. F. Beckenbach, McGraw-Hill, forthcoming.
- Richard Bellman,
*On some applications of the theory of dynamic programming to logistics*, Naval Res. Logist. Quart.**1**(1954), 141–153. MR**63636**, DOI https://doi.org/10.1002/nav.3800010209 - Richard Bellman,
*Some applications of the theory of dynamic programming—a review*, J. Operations Res. Soc. Amer.**2**(1954), 275–288. MR**62414** - Richard Bellman,
*Bottleneck problems, functional equations, and dynamic programming*, Econometrica**23**(1955), 73–87. MR**70935**, DOI https://doi.org/10.2307/1905582
15. R. Bellman, On a functional equation arising in the problem of optimal inventory, The RAND Corporation, Paper P-480, January 1954.
16. R. Bellman, Dynamic programming and the calculus of variations–I, The RAND Corporation, Paper P-495, March 1954.
- Richard Bellman,
*Dynamic programming of continuous processes*, The Rand Corporation, Santa Monica, Calif., 1954. MR**0071700** - Richard Bellman,
*Dynamic programming of continuous processes*, The Rand Corporation, Santa Monica, Calif., 1954. MR**0071700** - Richard Bellman and David Blackwell,
*Some two-person games involving bluffing*, Proc. Nat. Acad. Sci. U.S.A.**35**(1949), 600–605. MR**31700**, DOI https://doi.org/10.1073/pnas.35.10.600 - Richard Bellman, Irving Glicksberg, and Oliver Gross,
*On some variational problems occurring in the theory of dynamic programming*, Proc. Nat. Acad. Sci. U.S.A.**39**(1953), 298–301. MR**54183**, DOI https://doi.org/10.1073/pnas.39.4.298
21. R. Bellman, I. Glicksberg, and O. Gross, On some variational problems in the theory of dynamic programming, Rend. Circ. Mat. Palermo, forthcoming.
- R. Bellman, I. Glicksberg, and O. Gross,
*The theory of dynamic programming as applied to a smoothing problem*, J. Soc. Indust. Appl. Math.**2**(1954), 82–88. MR**67378** - Richard Bellman and Oliver Gross,
*Some combinatorial problems arising in the theory of multi-stage processes*, J. Soc. Indust. Appl. Math.**2**(1954), 175–183 (1955). MR**68193**
24. R. Bellman, T. E. Harris, and H. N. Shapiro, Studies on functional equations occurring in decision processes, The RAND Corporation, Paper P-382, August 1952.
- Richard Bellman and Shermann Lehman,
*On the continuous gold-mining equation*, Proc. Nat. Acad. Sci. U.S.A.**40**(1954), 115–119. MR**60681**, DOI https://doi.org/10.1073/pnas.40.2.115
26. R. Bellman and R. S. Lehman, On a functional equation in the theory of dynamic programming and its generalizations, The RAND Corporation, Paper P-433, January 1954.
27. R. Bellman and R. S. Lehman, Studies on bottleneck problems in production processes, The RAND Corporation, Paper P-492, February 1954.
28. R. R. Bush and C. F. Mosteller, A mathematical model for simple learning, Psychological Review vol. 58 (1951) pp. 313-325.
- A. Dvoretzky, J. Kiefer, and J. Wolfowitz,
*The inventory problem. I. Case of known distributions of demand*, Econometrica**20**(1952), 187–222. MR**47304**, DOI https://doi.org/10.2307/1907847 - A. Dvoretzky, A. Wald, and J. Wolfowitz,
*Elimination of randomization in certain statistical decision procedures and zero-sum two-person games*, Ann. Math. Statistics**22**(1951), 1–21. MR**39228**, DOI https://doi.org/10.1214/aoms/1177729689
31. W. K. Estes, Toward a statistical theory of learning, Psychological Review vol. 57 (1950) pp. 94-107.
32. M. M. Flood, On stochastic learning theory, The RAND Corporation, Paper P-353, December 1952.
33. S. Johnson, Optimal two- and three-stage production schedules with setup times included, The RAND Corporation, Paper P-402, May 1953.
34. S. Johnson and S. Karlin, On optimal sampling procedure for a problem of two populations–I, The RAND Corporation, Paper P-328, October 1952.
35. S. Karlin, A mathematical treatment of learning models–I, The RAND Corporation, Research Memorandum RM-921, September 1952.
36. S. Karlin, and H. N. Shapiro, Decision processes and functional equations, The RAND Corporation, Research Memorandum RM-933, September 1952.
37. M. Peisakoff, More on games of survival, The RAND Corporation, Research Memorandum RM-884, June 1952.
- Herbert Robbins,
*Some aspects of the sequential design of experiments*, Bull. Amer. Math. Soc.**58**(1952), 527–535. MR**50246**, DOI https://doi.org/10.1090/S0002-9904-1952-09620-8 - L. S. Shapley,
*Stochastic games*, Proc. Nat. Acad. Sci. U.S.A.**39**(1953), 1095–1100. MR**61807**, DOI https://doi.org/10.1073/pnas.39.10.1953 - Richard Bellman,
*Dynamic programming of continuous processes*, The Rand Corporation, Santa Monica, Calif., 1954. MR**0071700** - Richard Bellman,
*Some functional equations in the theory of dynamic programming*, Proc. Nat. Acad. Sci. U.S.A.**39**(1953), 1077–1082. MR**61806**, DOI https://doi.org/10.1073/pnas.39.10.1077
42. R. Bellman, An iterative procedure for the determination of the Perron root of a positive matrix, The RAND Corporation, Paper P-577.
43. R. Bellman, On a quasi-linear equation, The RAND Corporation, Paper P-575.
- Richard Bellman,
*Dynamic programming and a new formalism in the theory of integral equations*, Proc. Nat. Acad. Sci. U.S.A.**41**(1955), 31–34. MR**72365**, DOI https://doi.org/10.1073/pnas.41.1.31
45. R. Bellman, A problem in the sequential design of experiments, The RAND Corporation, Paper P-586.
- Richard Bellman,
*Decision making in the face of uncertainty. I*, Naval Res. Logist. Quart.**1**(1954), 230–232 (1955). MR**67446**, DOI https://doi.org/10.1002/nav.3800010311 - Richard Bellman,
*Decision making in the face of uncertainty. I*, Naval Res. Logist. Quart.**1**(1954), 230–232 (1955). MR**67446**, DOI https://doi.org/10.1002/nav.3800010311 - Richard Bellman,
*Some problems in the theory of dynamic programming*, Econometrica**22**(1954), 37–48. MR**60709**, DOI https://doi.org/10.2307/1909830
49. R. Bellman, I. Glicksberg, and O. Gross, On the optimal inventory equation, The RAND Corporation, Paper P-572.
50. R. Bellman, On some mathematical problems arising in the theory of optimal inventory and stock control, The RAND Corporation, Paper P-580.