Advertisement

Preliminary Concepts of Geometric Programming (GP) Model

  • Sahidul Islam
  • Wasim Akram Mandal
Chapter
Part of the Forum for Interdisciplinary Mathematics book series (FFIM)

Abstract

Geometric programming (GP) was introduced by Duffin, Peterson, and Zener in their famous book “Geometric programming” Theory and Application in 1967. It is natural to guess that the name “GP” comes from the many geometrical problems that can be formulated as GPs. But in fact, this comes from the arithmetic–geometric mean inequality (A.M.-G.M. inequality). This inequality plays a central role in the analysis of GPs.

References

  1. M. Bazaraa, C. Shetty, H. Sherali, Non-Linear Programming: Theory and Algorithms (Wiley, New York, 1993)zbMATHGoogle Scholar
  2. C.S. Beightler, D.T. Philips, Applied Geometric Programming (Wiley, New York, 1976)Google Scholar
  3. C. Chu, D. Wong, VLSI circuit performance optimization by geometric programming. Ann. Oper. Res. 105(1–4), 37–60 (2001)MathSciNetCrossRefGoogle Scholar
  4. R. Duffin, Linearizing geometric programs. SIAM Rev. 12(2), 668–675 (1970)MathSciNetCrossRefGoogle Scholar
  5. R. Duffin, E. Peterson, C. Zener, Geometric Programming—Theory and Application (Wiley, New York, 1967)zbMATHGoogle Scholar
  6. P. Feigin, U. Passy, The geometric programming dual to the extinction probability problem in simple branching processes. Ann. Probab. 9(3), 498–503 (1981)MathSciNetCrossRefGoogle Scholar
  7. C. Floudas, Deterministic Global Optimization: Theory, Algorithms and Applications (Kluwer Academic, Dordrecht, 1999)Google Scholar
  8. S. Islam, T.K. Roy, Modified Geometric programming problem and its applications, J. Appt. Math and comput, 17(1–2), 121–144 (2005). https://doi.org/10.1007/BF02936045MathSciNetCrossRefGoogle Scholar
  9. H. Jung, C. Klein, Optimal inventory policies under decreasing cost functions via geometric programming. Eur. J. Oper. Res. 132(3), 628–642 (2001)CrossRefGoogle Scholar
  10. E. Klafszky, J. Mayer, T. Terlaky, A geometric programming approach to the channel capacity problem. Eng. Optim. 19, 115–130 (1992)CrossRefGoogle Scholar
  11. E. Peterson, The origins of geometric programming. Ann. Oper. Res. 105(1–4), 15–19 (2001)MathSciNetCrossRefGoogle Scholar
  12. S.B. Sinha, A. Biswas, M.P. Biswal, Geometric programming problems with negative degrees of difficulty. Eur. J. Oper. Res. 28, 101–103 (1987)MathSciNetCrossRefGoogle Scholar
  13. C. Zener, Engineering Design by Geometric Programming (Wiley, New York, 1971)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Sahidul Islam
    • 1
  • Wasim Akram Mandal
    • 2
  1. 1.Department of MathematicsUniversity of KalyaniKalyani, NadiaIndia
  2. 2.Beldanga D.H. Senior MadrasahBeldanga, MurshidabadIndia

Personalised recommendations