Some functional equations in the theory of dynamic programming. I. Functions of points and point transformations
Author:
R. Bellman
Journal:
Trans. Amer. Math. Soc. 80 (1955), 5171
MSC:
Primary 39.0X
MathSciNet review:
0074692
Fulltext PDF Free Access
References 
Similar Articles 
Additional Information
 [1]
K. J. Arrow, T. E Harris, and J. Marschak, Optimal inventory policy, Cowles Commission Paper No. 44, 1951.
 [2]
Richard
Bellman, Bottleneck problems, functional equations, and dynamic
programming, Econometrica 23 (1955), 73–87. MR 0070935
(17,58e)
 [3]
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
(17,272d)
 [4]
Richard
Bellman, Stability theory of differential equations,
McGrawHill Book Company, Inc., New YorkTorontoLondon, 1953. MR 0061235
(15,794b)
 [5]
, A survey of the theory of boundedness, stability and asymptotic behavior of linear and nonlinear differential and difference equations, Office of Naval Research, 1949.
 [6]
, Dynamic programming, mathematics for modern engineers, ed. by E. F. Beckenbach, McGrawHill, Chapter 12, to appear.
 [7]
, Dynamic programming. A survey, Operations Research Quarterly vol. 2 (1954) pp. 275284.
 [8]
Richard
Bellman, On the theory of dynamic programming, Proc. Nat.
Acad. Sci. U. S. A. 38 (1952), 716–719. MR 0050856
(14,392b)
 [9]
Richard
Bellman, Some problems in the theory of dynamic programming,
Econometrica 22 (1954), 37–48. MR 0060709
(15,713c)
 [10]
Richard
Bellman, Some functional equations in the theory of dynamic
programming, Proc. Nat. Acad. Sci. U. S. A. 39
(1953), 1077–1082. MR 0061806
(15,887f)
 [11]
Richard
Bellman, The theory of dynamic
programming, Bull. Amer. Math. Soc. 60 (1954), 503–515. MR 0067459
(16,732c), http://dx.doi.org/10.1090/S000299041954098488
 [12]
, On the optimal inventory equation, Management Science (to appear).
 [13]
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
(15,804f)
 [14]
, On computational problems in the theory of dynamic programming, Proc. Symposium on Numerical Methods, Santa Monica, 1953, New York, McGrawHill, 1955.
 [15]
Richard
Bellman, Monotone approximation in dynamic programming and the
calculus of variations, Proc. Nat. Acad. Sci. U. S. A.
40 (1954), 1073–1075. MR 0067344
(16,714e)
 [16]
R. Bellman and D. Blackwell, On a particular nonzerosum game, September, 1949 (unpublished).
 [17]
R. Bellman and J. P. LaSalle, On nonzerosum games and stochastic processes, August, 1949 (unpublished).
 [18]
Richard
Bellman and Shermann
Lehman, On the continuous goldmining equation, Proc. Nat.
Acad. Sci. U. S. A. 40 (1954), 115–119. MR 0060681
(15,708c)
 [19]
, A functional equation in the theory of dynamic programming and its generalizations (submitted to Memoirs of the American Mathematical Society).
 [20]
A.
Dvoretzky, J.
Kiefer, and J.
Wolfowitz, The inventory problem. I. Case of known distributions of
demand, Econometrica 20 (1952), 187–222. MR 0047304
(13,856a)
 [1]
 K. J. Arrow, T. E Harris, and J. Marschak, Optimal inventory policy, Cowles Commission Paper No. 44, 1951.
 [2]
 R. Bellman, Bottleneck problems, functional equations and dynamic programming, Econometrica vol. 23 (1955) pp. 7387. MR 0070935 (17:58e)
 [3]
 , Dynamic programming and a new formalism in the theory of integral equations, Proc. Nat. Acad. Sci. U.S.A. vol. 41 (1955) pp. 3134. MR 0072365 (17:272d)
 [4]
 , Stability theory of differential equations, McGrawHill, 1953. MR 0061235 (15:794b)
 [5]
 , A survey of the theory of boundedness, stability and asymptotic behavior of linear and nonlinear differential and difference equations, Office of Naval Research, 1949.
 [6]
 , Dynamic programming, mathematics for modern engineers, ed. by E. F. Beckenbach, McGrawHill, Chapter 12, to appear.
 [7]
 , Dynamic programming. A survey, Operations Research Quarterly vol. 2 (1954) pp. 275284.
 [8]
 , The theory of dynamic programming, Nat. Proc. Acad. Sci. U.S.A. vol. 38 (1952) pp. 716719. MR 0050856 (14:392b)
 [9]
 , Some problems in the theory of dynamic programming, Econometrica vol. 22 (1954) pp. 3748. MR 0060709 (15:713c)
 [10]
 , Some functional equations in the theory of dynamic programming, Proc. Nat. Acad. Sci. U.S.A. vol. 39 (1953) pp. 10771082. MR 0061806 (15:887f)
 [11]
 , The theory of dynamic programming, Bull. Amer. Math. Soc. vol. 60 (1954) pp. 503515. MR 0067459 (16:732c)
 [12]
 , On the optimal inventory equation, Management Science (to appear).
 [13]
 , Dynamic programming and a new formalism in the calculus of variations, Proc. Nat. Acad. Sci. U.S.A. vol. 40 (1954) pp. 231235. MR 0061289 (15:804f)
 [14]
 , On computational problems in the theory of dynamic programming, Proc. Symposium on Numerical Methods, Santa Monica, 1953, New York, McGrawHill, 1955.
 [15]
 , Monotone convergence in dynamic programming and the calculus of variations, Proc. Nat. Acad. Sci. U.S.A. vol. 40 (1954) pp. 10731075. MR 0067344 (16:714e)
 [16]
 R. Bellman and D. Blackwell, On a particular nonzerosum game, September, 1949 (unpublished).
 [17]
 R. Bellman and J. P. LaSalle, On nonzerosum games and stochastic processes, August, 1949 (unpublished).
 [18]
 R. Bellman and S. Lehmann, On the continuous goldmining equation, Proc. Nat. Acad. Sci. U.S.A. vol. 40 (1954) pp. 115119. MR 0060681 (15:708c)
 [19]
 , A functional equation in the theory of dynamic programming and its generalizations (submitted to Memoirs of the American Mathematical Society).
 [20]
 A. J. Dvoretzky, J. Kiefer, and J. Wolfowitz, The inventory problemI: Case of known distributions of demand and The inventory problemII: Case of unknown distributions of Demand, Econometrica vol. 20 (1952) pp. 187222. MR 0047304 (13:856a)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947195500746920
PII:
S 00029947(1955)00746920
Article copyright:
© Copyright 1955
American Mathematical Society
