Skip to main content

On the Foundations of Dynamic Programming

  • Chapter
Topics in Combinatorial Optimization

Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 175))

Abstract

Dynamic programming is a technique for solving optimization problems introduced by Bellman [1]. This technique represents a problem as a process evolving from state to state through successive decisions. The problem then becomes one of finding an optimal policy, i.e. an optimal sequence of decisions, which can be obtained by solving a functional equation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

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

    MATH  Google Scholar 

  2. Denardo, E.V., Contraction Mapping in the Theory Underlying Dynamic Programming, SIAM Rev., 9, 1967, pp. 165–177.

    Article  MathSciNet  MATH  Google Scholar 

  3. Mitten, L.G., Composition Principles for Synthesis of Optimal Multistage Processes, Operations Res., 12, 1964, pp. 610–619.

    Article  MathSciNet  MATH  Google Scholar 

  4. Nemhauser, G.L., Introduction to Dynamic Programming, Wiley, New York, 1966.

    Google Scholar 

  5. Karp, R.M. and Held, M., Finite-State Processes and Dynamic Programming, SIAM J. Appl. Math., 15, 1967, pp. 693–718.

    MathSciNet  MATH  Google Scholar 

  6. Salomaa, A., Theory of Automata, Pergamon, 1969.

    Google Scholar 

  7. Ibaraki, T., Representation Theorems for Equivalent Optimization Problems, Information and Control, 21, N. 5, 1972, pp. 397–435.

    Article  MathSciNet  MATH  Google Scholar 

  8. Ibaraki, T., Solvable Classes of Discrete Dynamic Programming, J.Math. Anal. Appl., 43, 1973, pp. 642–693.

    Article  MathSciNet  MATH  Google Scholar 

  9. Nilsson, N.J., Problem-Solving Methods in Artificial Intelligence, McGraw--Hill, 1971.

    Google Scholar 

  10. Birkhoff, G., Lattice Theory, Am.Math.Soc., 1967.

    Google Scholar 

  11. Tarsky, A., A Lattice-Theoretical Fixpoint Theorem and its Applications, Pacific J. of Maths, 5, pp. 285–309.

    Google Scholar 

  12. Martelli, A. and Montanari, U., Problem Solving as a Foundation for Dynamic Programming, in preparation.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1975 CISM, Udine

About this chapter

Cite this chapter

Martelli, A., Montanari, U. (1975). On the Foundations of Dynamic Programming. In: Rinaldi, S. (eds) Topics in Combinatorial Optimization. CISM International Centre for Mechanical Sciences, vol 175. Springer, Vienna. https://doi.org/10.1007/978-3-7091-3291-3_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-7091-3291-3_9

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-81339-3

  • Online ISBN: 978-3-7091-3291-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics