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

**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**, 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.**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**, https://doi.org/10.1007/BF02847783**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**, https://doi.org/10.2307/1909830**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**, https://doi.org/10.1002/nav.3800010209**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**, 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.**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**, https://doi.org/10.2307/1907847**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**, https://doi.org/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**, https://doi.org/10.1002/nav.3800010311**47.**Richard Bellman,*Decision making in the face of uncertainty. I*, Naval Res. Logist. Quart.**1**(1954), 230–232 (1955). MR**0067446**, https://doi.org/10.1002/nav.3800010311**48.**Richard Bellman,*Some problems in the theory of dynamic programming*, Econometrica**22**(1954), 37–48. MR**0060709**, 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.

Additional Information

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