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

References | Additional Information

**1.**K. J. Arrow, D. Blackwell, and M. A. Girshick,*Bayes and minimax solutions of sequential decision problems*, Econometrica vol. 17 (1949) pp. 214-244. MR**32173****2.**K. J. Arrow, T. E. Harris, and J. Marschak,*Optimal inventory policy*, Cowles Commission Paper No. 44, 1951.**3.**R. Bellman,*An introduction to the theory of dynamic programming*, The RAND Corporation, Report R-245, 1953. MR**61805****4.**R. Bellman,*On games involving bluffing*, Rend. Circ. Mat. Palermo (2) vol. 1 (1952) pp.1-18. MR**53470****5.**R. Bellman,*On the theory of dynamic programming*, Proc. Nat. Acad. Sci. U.S.A. vol. 38 (1952) pp. 716-719. MR**50856****6.**R. Bellman,*Some problems in the theory of dynamic programming*, Econometrica vol. 22 (1954) pp. 37-48. MR**60709****7.**R. Bellman,*On bottleneck problems and dynamic programming*, Proc. Nat. Acad. Sci. U.S.A. vol. 39 (1953) pp. 947-951. MR**61808****8.**R. Bellman,*On computational problems in the theory of dynamic programming*, Symposium of Numerical Methods, Santa Monica, 1953, The RAND Corporation, Paper P-423. MR**61805****9.**R. Bellman,*Some functional equations in the theory of dynamic programming*, Proc. Nat. Acad. Sci. U.S.A. vol. 39 (1953) pp. 1077-1082. MR**61806****10.**R. Bellman,*Dynamic programming and a new formalism in the calculus of variations*, Proc. Nat. Acad. Sci. U.S.A. vol 40 (1954) pp. 231-235. MR**61289****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.**R. Bellman,*Some applications of the theory of dynamic programming to logistics*, Navy Quarterly of Logistics, September 1954. MR**63636****13.**R. Bellman,*Some applications of the theory of dynamic programming--a review*, Operations Research Quarterly, June 1954. MR**62414****14.**R. Bellman,*Bottleneck problems, functional equations, and dynamic programming*, The RAND Corporation, Paper P-483, January 1954; Econometrica (to appear). MR**70935****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.**R. Bellman,*Dynamic programming and the calculus of variations*--II, The RAND Corporation, Paper P-512, April 1954. MR**71700****18.**R. Bellman,*Monotone convergence in dynamic programming and the calculus of variations*, The RAND Corporation, Paper P-513, April 1954. MR**71700****19.**R. Bellman and D. Blackwell,*Some two-person games involving bluffing*, Proc. Nat. Acad. Sci. U.S.A. vol. 35 (1949) pp. 600-605. MR**31700****20.**R. Bellman, I. Glicksberg, and O. Gross,*On some variational problems occurring in the theory of dynamic programming*, Proc. Nat. Acad. Sci. U.S.A. vol. 39 (1953) pp. 298-301. MR**54183****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*, Journal of the Society for Industrial and Applied Mathematics, forthcoming. MR**67378****23.**R. Bellman and O. Gross,*Some combinatorial problems arising in the theory of multi-stage processes*, The RAND Corporation, Paper P-456, November 1953. 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.**25.**R. Bellman and R. S. Lehman,*On the continuous gold-mining equation*, Proc. Nat. Acad. Sci. U.S.A. vol. 40 (1954) pp. 115-119. MR**60681****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. J. Dvoretzky, J. Kiefer, and J. Wolfowitz,*The inventory problem*--I:*Case of known distributions of demand*, and*The inventory problem*--II:*Case of unknown distributions of demand*, Econometrica vol. 20 (1952) pp. 187-222. MR**47304****30.**A. J. Dvoretzky, A. Wald, and J. Wolfowitz,*Elimination of randomization in certain statistical decision procedures and zero-sum two-person games*, Ann. Math. Statist, vol. 22 (1951) pp. 1-21. MR**39228****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.**H. Robbins,*Some aspects of the sequential design of experiments*, Bull. Amer. Math. Soc. vol. 58 (1952) pp. 527-536. MR**50246****39.**L. Shapley,*Stochastic games*, Proc. Nat. Acad. Sci. U.S.A. vol. 39 (1953) pp. 1095-1100. MR**61807****40.**R. Bellman,*Dynamic programming and continuous processes*, The RAND Corporation, Report R-271, November 1954. MR**71700****41.**R. Bellman,*Some functional equations in the theory of dynamic programming--I, Point functions and point transformations*, The RAND Corporation, Paper P-566, September 1954. MR**61806****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.**R. Bellman,*Dynamic programming and a new formalism in the theory of integral equations*, Proc. Nat. Acad. Sci. U.S.A., to appear. MR**72365****45.**R. Bellman,*A problem in the sequential design of experiments*, The RAND Corporation, Paper P-586.**46.**R. Bellman,*Decision-making in the face of uncertainty*--I, Navy Quarterly of Logistics, September 1954. MR**67446****47.**R. Bellman,*Decision-making in the face of uncertainty*--II, Navy Quarterly of Logistics, December 1954. MR**67446****48.**R. Bellman,*Dynamic programming and multi-stage decision processes of stochastic type*, Symposium on Linear Programming, Washington, D. C., December, 1954. MR**60709****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