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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 

 

The theory of dynamic programming


Author: Richard Bellman
Journal: Bull. Amer. Math. Soc. 60 (1954), 503-515
MathSciNet review: 0067459
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  • 1. K. J. Arrow, D. Blackwell, and M. A. Girshick, Bayes and minimax solutions of sequential decision problems, Econometrica 17 (1949), 213–244. MR 0032173
  • 2. K. J. Arrow, T. E. Harris, and J. Marschak, Optimal inventory policy, Cowles Commission Paper No. 44, 1951.
  • 3. Richard Bellman, An introduction to the theory of dynamic programming, The Rand Corporation, Santa Monica, Calif., 1953. MR 0061805
  • 4. Richard Bellman, On games involving bluffing, Rend. Circ. Mat. Palermo (2) 1 (1952), 139–156. MR 0053470
  • 5. Richard Bellman, On the theory of dynamic programming, Proc. Nat. Acad. Sci. U. S. A. 38 (1952), 716–719. MR 0050856
  • 6. Richard Bellman, Some problems in the theory of dynamic programming, Econometrica 22 (1954), 37–48. MR 0060709
  • 7. Richard Bellman, Bottleneck problems and dynamic programming, Proc. Nat. Acad. Sci. U. S. A. 39 (1953), 947–951. MR 0061808
  • 8. Richard Bellman, An introduction to the theory of dynamic programming, The Rand Corporation, Santa Monica, Calif., 1953. MR 0061805
  • 9. Richard Bellman, Some functional equations in the theory of dynamic programming, Proc. Nat. Acad. Sci. U. S. A. 39 (1953), 1077–1082. MR 0061806
  • 10. 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 0061289
  • 11. R. Bellman, The theory of dynamic programming, a general survey, Chapter from "Mathematics for Modern Engineers" by E. F. Beckenbach, McGraw-Hill, forthcoming.
  • 12. Richard Bellman, On some applications of the theory of dynamic programming to logistics, Naval Res. Logist. Quart. 1 (1954), 141–153. MR 0063636
  • 13. Richard Bellman, Some applications of the theory of dynamic programming—a review, J. Operations Res. Soc. Amer. 2 (1954), 275–288. MR 0062414
  • 14. Richard Bellman, Bottleneck problems, functional equations, and dynamic programming, Econometrica 23 (1955), 73–87. MR 0070935
  • 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.
  • 17. Richard Bellman, Dynamic programming of continuous processes, The Rand Corporation, Santa Monica, Calif., 1954. MR 0071700
  • 18. Richard Bellman, Dynamic programming of continuous processes, The Rand Corporation, Santa Monica, Calif., 1954. MR 0071700
  • 19. Richard Bellman and David Blackwell, Some two-person games involving bluffing, Proc. Nat. Acad. Sci. U. S. A. 35 (1949), 600–605. MR 0031700
  • 20. 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 0054183
  • 21. R. Bellman, I. Glicksberg, and O. Gross, On some variational problems in the theory of dynamic programming, Rend. Circ. Mat. Palermo, forthcoming.
  • 22. 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 0067378
  • 23. 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 0068193
  • 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.
  • 25. Richard Bellman and Shermann Lehman, On the continuous gold-mining equation, Proc. Nat. Acad. Sci. U. S. A. 40 (1954), 115–119. MR 0060681
  • 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.
  • 29. A. Dvoretzky, J. Kiefer, and J. Wolfowitz, The inventory problem. I. Case of known distributions of demand, Econometrica 20 (1952), 187–222. MR 0047304
  • 30. 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 0039228
  • 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.
  • 38. Herbert Robbins, Some aspects of the sequential design of experiments, Bull. Amer. Math. Soc. 58 (1952), 527–535. MR 0050246, 10.1090/S0002-9904-1952-09620-8
  • 39. L. S. Shapley, Stochastic games, Proc. Nat. Acad. Sci. U. S. A. 39 (1953), 1095–1100. MR 0061807
  • 40. Richard Bellman, Dynamic programming of continuous processes, The Rand Corporation, Santa Monica, Calif., 1954. MR 0071700
  • 41. Richard Bellman, Some functional equations in the theory of dynamic programming, Proc. Nat. Acad. Sci. U. S. A. 39 (1953), 1077–1082. MR 0061806
  • 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.
  • 44. 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 0072365
  • 45. R. Bellman, A problem in the sequential design of experiments, The RAND Corporation, Paper P-586.
  • 46. Richard Bellman, Decision making in the face of uncertainty. I, Naval Res. Logist. Quart. 1 (1954), 230–232 (1955). MR 0067446
  • 47. Richard Bellman, Decision making in the face of uncertainty. I, Naval Res. Logist. Quart. 1 (1954), 230–232 (1955). MR 0067446
  • 48. Richard Bellman, Some problems in the theory of dynamic programming, Econometrica 22 (1954), 37–48. MR 0060709
  • 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.


Additional Information

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