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Functional equations in dynamic programming

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  1. Bellman, R.,Dynamic programming. Princeton University Press, Princeton, N.J., 1957.

    MATH  Google Scholar 

  2. Bellman, R.,Adaptive control processes. A guided tour. Princeton University Press, Princeton, N.J., 1961.

    Book  MATH  Google Scholar 

  3. Bellman, R. andDreyfus, S.,Applied dynamic programming. Princeton University Press, Princeton, N.J., 1962.

    Book  MATH  Google Scholar 

  4. Arrow, K. J., Karlin, S. andScarf, H.,Studies in the mathematical theory of inventory and production. Stanford University Press, Stanford, 1958.

    MATH  Google Scholar 

  5. Mine, H. andOsaki, S.,Markovian decision-processes. American Elsevier, New York, 1970.

    MATH  Google Scholar 

  6. Howard, R. A.,Dynamic programming and Markov processes. Wiley, 1960.

  7. Bellman, R.,Introduction to the mathematical theory of control processes, Volumes I and II, 1967, 1971. Academic Press, New York.

    MATH  Google Scholar 

  8. Dreyfus, S.,Dynamic programming and the calculus of variations. Academic Press, New York, 1965.

    MATH  Google Scholar 

  9. Aris, R.,Discrete dynamic programming. Blaisdell, New York, 1964.

    MATH  Google Scholar 

  10. Bellman, R. andAngel, E.,Dynamic programming and partial differential equations. Academic Press, New York, 1972.

    MATH  Google Scholar 

  11. Lee, E. S.,Quasilinearization and invariant imbedding. Academic Press, New York, 1968.

    MATH  Google Scholar 

  12. Bellman, R. andWing, G. M.,An introduction to invariant imbedding. Wiley, New York, 1975.

    MATH  Google Scholar 

  13. Wing, G. M.,An introduction to transport theory. Wiley, New York, 1962.

    Google Scholar 

  14. Bellman, R. andZadeh, L. A.,Decision-making in a fuzzy environment, Management Sciences 17, (1970), B-141–B164.

    Article  MathSciNet  MATH  Google Scholar 

  15. Bellman, R.,A note on cluster analysis and dynamic programming. Mathematical Biosciences 19 (1973), 311–312.

    Article  MathSciNet  MATH  Google Scholar 

  16. Chang, S. S. L.,Fuzzy dynamic programming and decision-making process. InProceedings of the 3rd Princeton Conference on Information Sciences, 1969, pp. 200–203.

  17. Zadeh, L. A.,Fuzzy sets. Information and Control,8 (1965), 338–353.

    Article  MathSciNet  MATH  Google Scholar 

  18. Zadeh, L. A.,Fuzzy algorithms. Information and Control12 (1968), 94–102.

    Article  MathSciNet  MATH  Google Scholar 

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This research was supported by the National Science Foundation under Grant No. MPS-74-15650 and the Energy Research and Development Administration (ERDA) under Contract No. E(04–3)113, Project 19.

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Bellman, R., Lee, E.S. Functional equations in dynamic programming. Aequat. Math. 17, 1–18 (1978).

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