DYNAMIC PROGRAMMING

Dynamic Programming

Volumn , Issue , 2021, Pages 1-346

  Bellman, Richard ^a  

^a NONE

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EID: 85012688561     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Book

References (72)

1. R. Bellman, “The Theory of Dynamic Programming,” Bull. Amer. Math. Soc, vol. 60 (1954), pp. 503-516.
2. Econometrica, vol. 22 (1954), pp. 37-48.
3. R. Bellman, “A Class of Variational Problems,” Quart, of Appl. Math., 1956.
4. I. J. Schoenberg, “On Smoothing Functions and their Generating Functions,” Bull. Amer. Math. Soc, vol. 59 (1953), pp. 199-230
5. R. Bellman, “On Computational Problems in the Theory of Dynamic Programming,” Symposium on Numerical Methods, Amer. Math. Soc. Santa Monica, 1953.
6. R. Bellman, Stability Theory of Differential Equations, McGraw-Hill, 1954.
7. J. Kiefer, “Sequential Minimax Search for a Maximum,” Proc. Amer. Math. Soc, vol. 4 (1953), pp. 502-6.
8. W. Feller, Probability Theory, John Wiley and Sons, 1948.
9. M. S. Bartlett, An introduction to stochastic processes with special reference to methods and applications, Cambridge, 1955.
10. K. D. Arrow, D. Blackwell, M. Girshick, “Bayes and Minimax Solutions of Sequential Decision Problems,” Econometrica, vol. 17 (1949), pp. 213-214.
11. S. Karlin and H. N. Shapiro, “Decision Processes and Functional Equations,” RM-933, Sept. 1952
12. R. Bellman and R. Kalaba, “On the Principle of Invariant Imbedding and Propagation Through Inhomogeneous Media,” Proc. Nat. Acad. Sci., (1956)
13. Ambarzumian “On the Scattering of Light by a Diffuse Medium,” C. R. Doklady, Sci. U.R.S.S. 38 (1943), p. 257
14. S. Chandrasekhar Radiative Transfer, Oxford, 1950
15. R. Bellman and T. E. Harris, “On Age-Dependent Binary Branching Processes,” Ann. Math., Vol. 55 (1952), pp. 280-295.
16. J. Hadamard, “Le principe de Huygens,” Bull. Soc. Math. France, 52 (1924), pp. 610-640
17. E. Hille, “Functional Analysis and Semi-groups,” Amer. Math. Soc, 1948.
18. R. Bellman, “Dynamic Programming and A New Formalism in the Theory of Integral Equations,” Proc. Nat. Acad. Sci., Vol. 41 (1955), pp. 31-34.
19. R. Bellman, “Dynamic Programming and Lagrange Multipliers”, Proc. Nat. Acad. Sci., Vol. 42 (1956), pp. 767-769.
20. R. Bellman, “Functional equations in the Theory of Dynamic Programming - I, Functions of Points and Point Transformations,” Trans. Amer. Math. Soc, vol., Vol. 80 (1955), pp. 51-71.
21. S. Karlin and H. N. Shapiro, “Decision Processes and Functional Equations.” The RAND Corporation, RM-933, Sept. 1952.
22. S. Karlin, “The Structure of Dynamic Programming Models,” Naval Research Logistics Quarterly, Vol 2 (1955), pp. 285-294.
23. R. Bellman, Stability Theory of Differential Equations, McGraw-Hill, 1952.
24. K. D. Arrow, T. E. Harris and J. Marschak, “Optimal Inventory Policy,” Econometrica, July, 195
25. A. Dvoretsky, J. Kiefer and J. Wolfowitz, “The Inventory Problem I, II,” Econometrica, vol. 20 (1952), pp. 187-222.
26. I. Glicksberg and O. Gross, R. Bellman, I. Glicksberg and O. Gross, “On the Optimal Inventory Equation,” Management Science, vol. 2 (1955), pp. 83-104.
27. W. Feller, “On the Integral Equation of Renewal Theory,” Ann. Math. Stat., vol. 12 (1941)
28. R. Bellman, (with the collaboration of J. M. Danskin), “A Survey of the Theory of Time-Lag, Retarded Control and Hereditary Processes,” RAND Corporation, 1954, R-271.
29. R. Bellman, “Bottleneck Problems and Dynamic Programming,” Proc. Nat. A cad. Set., vol. 39 (1953)
30. R. Bellman, “Bottleneck Problems, Functional Equations and Dynamic Programming,” Econometrica, vol. 23 (1955), pp. 73-87.
31. R. S. Lehman, “On the Continuous Simplex Method” RM-1386, RAND Corporation, 1954.
32. R. Bellman and R. S. Lehman, Studies on Bottleneck Problems in Production Processes, Part I, P-492, RAND Corporation, 1954.
33. R. S. Lehman, Studies in Bottleneck Problems in Production Processes, Part II, P-492, RAND Corporation, 1954.
34. R. Bellman and R. S. Lehman, “On the Continuous Gold-Mining Equation,” Proc. Nat. Acad. Set., vol. 40 (1954), pp. 115-119
35. R. Bellman and R. S. Lehman, “On a Functional Equation in the Theory of Dynamic Programming and its Generalizations,” (unpublished)
36. J. L. Doob, Stochastic Processes, J. Wiley and Sons, (1953)
37. R. Bellman and D. Blackwell, “Some two-person games involving bluffing,” Proc. Nat. Acad. Sci., vol. 35 (1949), pp. 600-5
38. R. Bellman, “On Games Involving Bluffing,” Rend. Circ. Mat. Palermo (2), vol. 1 (1952), pp. 1-18.
39. H. Osborn, “On the Convergence of Discrete Stochastic Processes to their Continuous Analogues,” RM-1368, RAND Corporation, (1955)
40. H. Osborn, “The Problem of Continuous Programs,” P-718, Rand Corporation, (1955).
41. Pac. Jour. Math., Vol. 6 (1956), pp. 721-731.
42. R. Bellman, “Dynamic Programming and a new formalism in the calculus of variations,” Proc. Nat. Acad. Sci., vol. 39 (1953), pp. 1077-1082.
43. R. Bellman, “On the Application of Dynamic Programming to Variational Problems arising in Mathematical Economics” Proc. Symposium on Calculus of Variations and Applications, Chicago, 1956.
44. R. Bellman, W. Fleming and D. V. Widder, “Variational Problems Involving Constraints” Annali di Matematica, 1956.
45. R. Bellman, “Notes on the Theory of Dynamic Programming,” Jour. Soc. Ind. Appl. Math., 1955.
46. R. Bellman, “Functional Equations in the Theory of Dynamic Programming-VI, A Direct Convergence Proof,” Annals of Math., 1957.
47. R. Bellman, “Dynamic Programming of Continuous Processes”. The RAND Corporation, R-271, 1954.
48. R. Bellman, “Monotone Approximation in Dynamic Programming and the Calculus of Variations,” Proc. Nat. Acad. Sci., vol. 40 (1954), pp. 1073-5.
49. R. Bellman, “On the Application of Dynamic Programming to the Study of Control Processes,” Proc. Symposium on Nonlinear Control Processes, Bklyn Polytechnic Inst., 1956.
50. J. D. Williams, The Compleat Strategyst, McGraw-Hill, 1955.
51. R. Bellman and D. Blackwell, “Red Dog, Blackjack and Poker,” Scientific American, vol. 184 (1951), pp. 44-47
52. A. Wald, Statistical Decision Functions, J. Wiley and Sons, 1950
53. D. Blackwell and A. Girshick, Theory of Games and Statistical Decisions, J. Wiley and Sons, 1954
54. H. Robbins, “Some Aspects of the Sequential Design of Experiments,” Bull. Amer. Math. Soc, vol. 58 (1952), pp. 527-536.
55. J. F. Nash, “Equilibrium Points in Af-person Games,” Proc. Nat. Acad. Sci., vol. 36 (1950), pp. 48-9.
56. S. Karlin, “The Theory of Infinite Games,” Annals of Math., 1951
57. M. Dresher and S. Karlin, “Solutions of Convex Games as Fixed Points,” Contributions to the Theory of Games 11, Annals of Mathematics Study No. 28, Princeton University Press, 1951.
58. R. Bellman and J. P. LaSalle, “On Non-Zero Sum Games and Stochastic Processes,” RM-212, The RAND Corporation, 1949
59. R. Bellman and D. Blackwell, “On a Particular Non-Zero Sum Game,” RM-250, The RAND Corporation, 1949.
60. R. Isaacs, “The Problem of Aiming and Evasion,” P-642, The RAND Corporation, 1955
61. R. Isaacs, “Differential Games-I, II, III, IV,” RM-1391, 1399, 1411, 1486, The RAND Corporation, 1955.
62. L. Shapley, “Stochastic Games,” Proc. Nat. Acad. Sci., vol. 39 (1953), pp. 1095-1100.
63. M. Peisakoff, “More on Games of Survival,” RM-884, The RAND Corporation, 1952
64. J. Milnor and L. Shapley, “On Games of Survival,” P-622, The RAND Corporation, 1955.
65. R. Bellman, “Decision Making in the Face of Uncertainty-II, " Naval Research Logistics Quarterly, vol. 1 (1954), pp. 323-332.
66. R. Bellman, “Functional Equations in the Theory of Dynamic Programming-IV, Multi-Stage Decision Processes of Continuous Type,” Rand Paper p. 705, June 1955.
67. W. Feller, Probability Theory, John Wiley and Sons, 1948.
68. R. Bellman, “Functional Equations in the Theory of Dynamic Programming-II, Nonlinear Differential Equations,” Proc. Nat. Acad. Sci., vol. 41 (1955), pp. 482-5.
69. R. Bellman, “The Stability of Solutions of Linear Differential Equations,” Duke Math. Jour., vol. 10 (1943), pp. 643-7
70. R. Bellman, “Functional Equations in the Theory of Dynamic Programming-V, Positivity and Linearity,” Proc. Nat. Acad. Sci., vol. 41 (1955), pp. 743-6
71. R. Bellman, “On the Explicit Solutions of Some Algebraic Equations,” Math. Mag., 1956.
72. R. Bellman, “On a Class of Quasi-Linear Equations,” Can. Jour. of Math., 1956.