Skip to main content
SpringerLink
Log in

Entropy Optimization Models

  • Chapter
Book cover Entropy Optimization and Mathematical Programming

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 8))

Abstract

Entropy optimization models have been successfully applied to practical problems in many scientific and engineering disciplines. As noted in Chapter 1, those disciplines include statistical mechanics, thermodynamics, statistical parameter estimation and inference, economics, business and finance, nonlinear spectral analysis, pattern recognition, transportation, urban and regional planning, queueing theory, and linear and nonlinear programming. Included in this book are example applications in the areas of (1) queueing theory, (2) transportation planning, (3) input-output analysis, (4) regional planning, (5) investment portfolio optimization, and (6) image reconstruction. They are discussed in six sections, from Sections 2.1 through 2.6.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover 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. Alonso, W., “A Theory of the Urban Land Market,” Papers of the Regional Science Association, Vol. 6, 1960, pp. 146–158.

    Google Scholar 

  2. Alonso, W., Location and Land Use, Harvard University Press, Cambridge, Massachusetts, 1964.

    Google Scholar 

  3. Bregman, L.M., “The Relaxation Method of Finding the Common Point of Convex Sets and Its Application to the Solution of Problems in Convex Programming,” U.S.S.R. Computational Mathematics and Mathematical Physics, Vol. 7, 1967, pp. 200–217.

    Article  Google Scholar 

  4. Brice, S., “Derivation of Nested Transport Models within a Mathematical Programming Framework,” Transportation Research Part B, Vol. 23B, 1989, pp. 19–28.

    Article  Google Scholar 

  5. Burch, S.F., Gull, S.F., and Skilling, J.K., “Image Restoration by a Powerful Maximum Entropy Method,” Computer Vision, Graphics, and Image Processing, Vol. 23, 1983, pp. 113–128.

    Article  Google Scholar 

  6. Censor, Y., and Herman, G.T., “On Some Optimization Techniques in Image Reconstruction,” Applied Numerical Mathematics, Vol. 3, 1987, pp. 365–391.

    Article  Google Scholar 

  7. Cottle, R.W., “Application of a Block Successive Overrelaxation Method to a Class of Constrained Matrix Problems,” Proceedings of the International Congress on Mathematical Programming, edited by R.W. Cottle, M.L. Kelmanson, and B. Korte, Rio de Janeiro, Brazil, April, 1981, pp. 89–103.

    Google Scholar 

  8. El-Affendi, M.A., and Kouvatsos, D.D., “A Maximum Entropy Analysis of the M/G/1 and G/M/1 Queueing System at Equilibrium,” Acta Informatica, Vol. 19, 1983, pp. 339–355.

    Article  Google Scholar 

  9. Elton, E.D., and Gruber, M.J., Modern Portfolio Theory and Investment Analysis, 4th Edition, John Wiley, New York, 1991.

    Google Scholar 

  10. Eriksson, J.R., “A Note on Solution of Large Sparse Maximum Entropy Problems with Linear Equality Constraints,” Mathematical Programming, Vol. 18, 1980, pp. 146–154.

    Article  Google Scholar 

  11. Erlander, S., “Efficient Population Behavior and the Simultaneous Choices of Origins, Destinations and Routes,” Transportation Research Part B, Vol. 24B, 1990, pp. 363–373.

    Article  Google Scholar 

  12. Erlander, S., and Stewart, N.F., The Gravity Model in Transportation Analysis, VSP, The Netherlands, 1990.

    Google Scholar 

  13. Erlang, A.K., “Theory of Probabilities and Telephone Conversations,” Nyt Tidsskrift Matematik, Vol. B-20, 1909, pp. 33–39.

    Google Scholar 

  14. Fang, S.-C., and Tsao, H.-S.J., “An Unconstrained Convex Programming Approach to Solving Convex Quadratic Programming Problems,” Optimization, Vol. 27, 1993, pp. 235–243.

    Article  Google Scholar 

  15. Fang, S.-C., and Tsao, H.-S.J., “Linear-Constrained Entropy Maximization Problem with Quadratic Cost and Its Applications to Transportation Planning Problems,” Transportation Science, Vol. 29, 1995, pp. 353–365.

    Article  Google Scholar 

  16. Ferdinand, A.E., “A Statistical Mechanics Approach to System Analysis,” IBM Journal of Research and Development, Vol. 14, 1970, pp. 539–547.

    Article  Google Scholar 

  17. Golan, A., Judge, G., and Robinson, S., “Recovering Information from Incomplete or Partial Multi-sectoral Economic Data,” Review of Economics and Statistics, Vol. LXXVI, 1994, pp. 541–549.

    Article  Google Scholar 

  18. Gross, D., and Harris, C.M., Fundamentals of Queueing Theory, 2nd Edition, John Wiley, New York, 1985.

    Google Scholar 

  19. Guiasu, S., “Maximum Entropy Condition in Queueing Theory,” Journal of Operational Research Society, Vol. 37, 1986, pp. 293–301.

    Google Scholar 

  20. Herman, G.T., “A Relaxation Method for Reconstructing Objects from Noisy X-Rays,” Mathematical Programming, Vol. 8, 1975, pp. 1–19.

    Article  Google Scholar 

  21. Herman, G.T., editor, Image Reconstruction from Projections: Implementation and Applications, Springer-Verlag, Berlin, 1979.

    Google Scholar 

  22. Herbert, D.J., and Stevens, B.H., “A Model for the Distribution of Residential Activity in Urban Areas,” Journal of Regional Science, Vol. 2, 1960, pp. 21–36.

    Article  Google Scholar 

  23. Jaynes, E.T., “Information Theory and Statistical Mechanics,” Physics Review, Vol. 106, 1957, pp. 620–630.

    Article  Google Scholar 

  24. Johnston, R.J., and Pattie, C.J., “Using Entropy-Maximizing Procedure to Estimate Territorial Social Indicators: An Introduction and Illustration,” Social Indicators Research, Vol. 27, 1992, pp. 235–256.

    Google Scholar 

  25. Jornsten, K.O., “An Algorithm for the Combined Distribution and Assignment Problem,” Transportation Research Part B, Vol. 15B, 1981, pp. 21–33.

    Article  Google Scholar 

  26. Jornsten, K.O., and Lundgren, J.T., “An Entropy-Based Model Split Model,” Transportation Research Part B, Vol. 23B, 1989, pp. 345–359.

    Article  Google Scholar 

  27. Kapur, J.N., Maximum-Entropy Models in Science and Engineering, Wiley Eastern Ltd., New Delhi, 1989.

    Google Scholar 

  28. Leontief, W., “Quantitative Input-Output Relations in the Economic System of the United States,” Review of Economic and Statistics, Vol. 18, 1936, pp. 105–125.

    Article  Google Scholar 

  29. Leontief, W., Input-Output Economics, 2nd Edition, Oxford University Press, New York, 1986.

    Google Scholar 

  30. Macgill, S.M., “Theoretical Properties of Bi-proportional Matrix Adjustments,” Environment and Planning A, Vol. 9, 1977, pp. 687–701.

    Article  Google Scholar 

  31. Markowitz, H.M., Portfolio Selection: Efficient Diversification of Investments, John Wiley, New York, 1959.

    Google Scholar 

  32. Miller, R.E., and Blair, P.D., Input-Output Analysis: Foundations and Extensions, Prentice Hall, New Jersey, 1985.

    Google Scholar 

  33. Mishra, S., and Fang, S.-C., “A Maximum Entropy Optimization Approach to Tandem Queues with Generalized Blocking,” Performance Evaluation, Vol. 702, 1997, pp. 1–25.

    Google Scholar 

  34. Safwat, K.N.A., and Magnanti, T.L., “A Combined Trip Generation, Trip Distribution, Modal Split, and Trip Assignment Model,” Transportation Science, Vol. 22, 1988, pp. 14–30.

    Article  Google Scholar 

  35. Schneider, M.H., and Zenios, S.A., “Comparative Study of Algorithms for Matrix Balancing,” Operations Research, Vol. 38, 1990, pp. 439–455.

    Article  Google Scholar 

  36. Scott, C.H., and Jefferson, T.R., “Entropy Maximizing Models of Residential Location via Geometric Programming,” Geographical Analysis, Vol. 9, 1977, pp. 181–187.

    Article  Google Scholar 

  37. Sen, A., and Smith, T.E., Gravity Models of Spatial Interaction Behavior, Springer-Verlag, Berlin, 1995.

    Book  Google Scholar 

  38. Sengupta, J.K., “Mixed Strategy and Information Theory in Optimal Portfolio Choice,” International Journal of Systems Science, Vol. 20, 1989, pp. 215–227.

    Article  Google Scholar 

  39. Senior, M.L., and Wilson, A.G., “Exploration and Synthesis of Linear Programming and Spatial Interaction Models of Residential Location,” Geographical Analysis, Vol. 6, 1974, pp. 209–238.

    Article  Google Scholar 

  40. Shore, J.E., “Information Theoretic Approximations for M/G/1 and G/G/1 Queueing Systems,” Acta Informatica, Vol. 17, 1982, pp. 47–61.

    Article  Google Scholar 

  41. Stark, H., editor, Image Recovery: Theory and Application, Academic Press, Orlando, Florida, 1987.

    Google Scholar 

  42. Takahashi, Y., and Takami, Y., “A Numerical Method for the Steady-State Probabilities of a G1/G/C Queue in a General Class,” Journal of Operations Research Society of Japan, Vol. 19, 1976, pp. 147–157.

    Google Scholar 

  43. Tomlin, J.A., “A Mathematical Programming Model for the Combined Distribution-Assignment of Traffic,” Transportation Science, Vol. 5, 1971, pp. 122–140.

    Article  Google Scholar 

  44. Tomlin, J.A., and Tomlin, S.G., “Traffic Distribution and Entropy,” Nature, Vol. 220, 1968, pp. 974–976.

    Article  Google Scholar 

  45. Viel, V.Q., “Practices in Input-Output Table Compilation,” Regional Science and Urban Economics, Vol. 24, 1994, pp. 27–54.

    Article  Google Scholar 

  46. Wang, Y., and Lu, W., “Multicriterion Maximum Entropy Image Reconstruction from Projections,” IEEE Transactions on Medical Imaging, Vol. 11, 1992, pp. 70–75.

    Article  Google Scholar 

  47. Wilson, A.G., “A Statistical Theory of Spatial Distribution Models,” Transportation Research, Vol. 1, 1967, pp. 253–269.

    Article  Google Scholar 

  48. Wilson, A.G., Entropy in Urban and Regional Planning, Pion, London, 1970.

    Google Scholar 

  49. Wilson, A.G., Urban and Regional Models in Geography and Planning, John Wiley, London, 1974.

    Google Scholar 

  50. Wu, J.-S., and Chan, W.C., “Maximum Entropy Analysis of Multiple-Server Queueing Systems,” Journal of Operational Research Society, Vol. 40, 1989, pp. 815–826.

    Google Scholar 

  51. Wu, J-S., “Maximum Entropy Analysis of Open Queueing Networks with Group Arrivals,” Journal of Operational Research Society, Vol. 43, 1992, pp. 1063–1078.

    Google Scholar 

  52. Yamada, M., and Rajasekera, J.R., “Portfolio Re-balancing with the Entropy Criteria,” Report No. 310, QUICK Research Institute Corp., Tokyo, 1993.

    Google Scholar 

  53. Zhuang, X., Haralick, R.M., and Zhao, Y., “Maximum Entropy Image Reconstruction,” IEEE Transactions on Signal Processing, Vol. 39, 1991, pp. 1478–1480.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. North Carolina State University, Raleigh, North Carolina, USA

    S.-C. Fang

  2. International University of Japan, Urasa, Niigata, Japan

    J. R. Rajasekera

  3. University of California, Berkeley, California, USA

    H.-S. J. Tsao

Authors
  1. S.-C. Fang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. R. Rajasekera
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H.-S. J. Tsao
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer Science+Business Media New York

About this chapter

Cite this chapter

Fang, SC., Rajasekera, J.R., Tsao, HS.J. (1997). Entropy Optimization Models. In: Entropy Optimization and Mathematical Programming. International Series in Operations Research & Management Science, vol 8. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-6131-6_2

Download citation

  • DOI: https://doi.org/10.1007/978-1-4615-6131-6_2

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7810-5

  • Online ISBN: 978-1-4615-6131-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation