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The theory of dynamic programming. (English) Zbl 0057.12503


MSC:

90C39 Dynamic programming

Citations:

Zbl 0051.37402
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Full Text: DOI

References:

[1] K. J. Arrow, D. Blackwell, and M. A. Girshick, Bayes and minimax solutions of sequential decision problems, Econometrica 17 (1949), 213 – 244. · Zbl 0034.07504 · doi:10.2307/1905525
[2] K. J. Arrow, T. E. Harris, and J. Marschak, Optimal inventory policy, Cowles Commission Paper No. 44, 1951. · Zbl 0045.23205
[3] Richard Bellman, An introduction to the theory of dynamic programming, The Rand Corporation, Santa Monica, Calif., 1953. · Zbl 0051.37402
[4] Richard Bellman, On games involving bluffing, Rend. Circ. Mat. Palermo (2) 1 (1952), 139 – 156. · Zbl 0047.37701 · doi:10.1007/BF02847783
[5] Richard Bellman, On the theory of dynamic programming, Proc. Nat. Acad. Sci. U. S. A. 38 (1952), 716 – 719. · Zbl 0047.13802
[6] Richard Bellman, Some problems in the theory of dynamic programming, Econometrica 22 (1954), 37 – 48. · Zbl 0057.12504 · doi:10.2307/1909830
[7] Richard Bellman, Bottleneck problems and dynamic programming, Proc. Nat. Acad. Sci. U. S. A. 39 (1953), 947 – 951. · Zbl 0053.27903
[8] Richard Bellman, An introduction to the theory of dynamic programming, The Rand Corporation, Santa Monica, Calif., 1953. · Zbl 0051.37402
[9] Richard Bellman, Some functional equations in the theory of dynamic programming, Proc. Nat. Acad. Sci. U. S. A. 39 (1953), 1077 – 1082. · Zbl 0051.37403
[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. · Zbl 0058.36303
[11] R. Bellman, The theory of dynamic programming, a general survey, Chapter from ”Mathematics for Modern Engineers” by E. F. Beckenbach, McGraw-Hill, forthcoming. · Zbl 0218.49012
[12] Richard Bellman, On some applications of the theory of dynamic programming to logistics, Naval Res. Logist. Quart. 1 (1954), 141 – 153. · doi: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.
[14] Richard Bellman, Bottleneck problems, functional equations, and dynamic programming, Econometrica 23 (1955), 73 – 87. · Zbl 0064.39502 · doi: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. · Zbl 0058.36304
[17] Richard Bellman, Dynamic programming of continuous processes, The Rand Corporation, Santa Monica, Calif., 1954. · Zbl 0057.12503
[18] Richard Bellman, Dynamic programming of continuous processes, The Rand Corporation, Santa Monica, Calif., 1954. · Zbl 0057.12503
[19] Richard Bellman and David Blackwell, Some two-person games involving bluffing, Proc. Nat. Acad. Sci. U. S. A. 35 (1949), 600 – 605. · Zbl 0041.44805
[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. · Zbl 0050.36807
[21] R. Bellman, I. Glicksberg, and O. Gross, On some variational problems in the theory of dynamic programming, Rend. Circ. Mat. Palermo, forthcoming. · Zbl 0050.36807
[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. · Zbl 0058.35901
[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). · Zbl 0058.36402
[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. · Zbl 0058.36302
[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. · Zbl 0046.37603 · doi: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. · Zbl 0044.15003
[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. · Zbl 0049.37009
[39] L. S. Shapley, Stochastic games, Proc. Nat. Acad. Sci. U. S. A. 39 (1953), 1095 – 1100. · Zbl 0051.35805
[40] Richard Bellman, Dynamic programming of continuous processes, The Rand Corporation, Santa Monica, Calif., 1954. · Zbl 0057.12503
[41] Richard Bellman, Some functional equations in the theory of dynamic programming, Proc. Nat. Acad. Sci. U. S. A. 39 (1953), 1077 – 1082. · Zbl 0051.37403
[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. · Zbl 0148.06302
[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. · Zbl 0068.13605
[45] R. Bellman, A problem in the sequential design of experiments, The RAND Corporation, Paper P-586. · Zbl 0075.14801
[46] Richard Bellman, Decision making in the face of uncertainty. I, Naval Res. Logist. Quart. 1 (1954), 230 – 232 (1955). · doi:10.1002/nav.3800010311
[47] Richard Bellman, Decision making in the face of uncertainty. I, Naval Res. Logist. Quart. 1 (1954), 230 – 232 (1955). · doi:10.1002/nav.3800010311
[48] Richard Bellman, Some problems in the theory of dynamic programming, Econometrica 22 (1954), 37 – 48. · Zbl 0057.12504 · doi:10.2307/1909830
[49] R. Bellman, I. Glicksberg, and O. Gross, On the optimal inventory equation, The RAND Corporation, Paper P-572. · Zbl 0995.90501
[50] R. Bellman, On some mathematical problems arising in the theory of optimal inventory and stock control, The RAND Corporation, Paper P-580.
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