Some functional equations in the theory of dynamic programming. I. Functions of points and point transformations
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- Trans. Amer. Math. Soc. 80 (1955), 51-71 Request permission
References
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K. J. Arrow, T. E Harris, and J. Marschak, Optimal inventory policy, Cowles Commission Paper No. 44, 1951.
- Richard Bellman, Bottleneck problems, functional equations, and dynamic programming, Econometrica 23 (1955), 73–87. MR 70935, DOI 10.2307/1905582
- 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 10.1073/pnas.41.1.31
- Richard Bellman, Stability theory of differential equations, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1953. MR 0061235 —, A survey of the theory of boundedness, stability and asymptotic behavior of linear and nonlinear differential and difference equations, Office of Naval Research, 1949. —, Dynamic programming, mathematics for modern engineers, ed. by E. F. Beckenbach, McGraw-Hill, Chapter 12, to appear. —, Dynamic programming. A survey, Operations Research Quarterly vol. 2 (1954) pp. 275-284.
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- Richard Bellman, Some problems in the theory of dynamic programming, Econometrica 22 (1954), 37–48. MR 60709, DOI 10.2307/1909830
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- Richard Bellman, The theory of dynamic programming, Bull. Amer. Math. Soc. 60 (1954), 503–515. MR 67459, DOI 10.1090/S0002-9904-1954-09848-8 —, On the optimal inventory equation, Management Science (to appear).
- 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 10.1073/pnas.40.4.231 —, On computational problems in the theory of dynamic programming, Proc. Symposium on Numerical Methods, Santa Monica, 1953, New York, McGraw-Hill, 1955.
- Richard Bellman, Monotone approximation in dynamic programming and the calculus of variations, Proc. Nat. Acad. Sci. U.S.A. 40 (1954), 1073–1075. MR 67344, DOI 10.1073/pnas.40.11.1073 R. Bellman and D. Blackwell, On a particular non-zero-sum game, September, 1949 (unpublished). R. Bellman and J. P. LaSalle, On non-zero-sum games and stochastic processes, August, 1949 (unpublished).
- 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 10.1073/pnas.40.2.115 —, A functional equation in the theory of dynamic programming and its generalizations (submitted to Memoirs of the American Mathematical Society).
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Additional Information
- © Copyright 1955 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 80 (1955), 51-71
- MSC: Primary 39.0X
- DOI: https://doi.org/10.1090/S0002-9947-1955-0074692-0
- MathSciNet review: 0074692