Encyclopedia of Operations Research and Management Science

2001 Edition
| Editors: Saul I. Gass, Carl M. Harris

Geometric programming

  • Joseph G. Ecker
Reference work entry
DOI: https://doi.org/10.1007/1-4020-0611-X_384

INTRODUCTION

Early work in geometric programming was stimulated by Zener ( 1961, 1962) in his investigation of cost minimization techniques for engineering design problems. Subsequent work by Duffin (1962), Duffin and Peterson (1966), and Duffin, Peterson, and Zener (1967) provided the fundamental groundwork of the subject. Geometric programming refers to a class of optimization problems that have the form
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References

  1. [1]
    Avriel, M., R. Dembo, and U. Passy (1975). “Solution of Generalized Geometric Programs,” Internat. Jl. Numer. Methods Engrg., 9, 149–169.Google Scholar
  2. [2]
    Avriel, M. and Williams, A.C. (1970). “Complementary Geometric Programming,” SIAM Jl. Appl. Math., 19, 125–141.Google Scholar
  3. [3]
    Beck, P.A. and Ecker, J.G. (1975). “A Modified Concave Simplex Algorithm for Geometric Programming,” Jl. Optimization Theory Appl., 15, 189–202.Google Scholar
  4. [4]
    Blau, G.E. and Wilde, D.J. (1971). “A Lagrangian Algorithm for Equality Constrained Generalized Polynomial Optimization,” AI Ch. E. Jl., 17, 235–240.Google Scholar
  5. [5]
    Blau, G.E. and Wilde, D.J. (1969). “Generalized Polynomial Programming,” Canad. Jl. Chemical Engineering, 47, 317–326.Google Scholar
  6. [6]
    Dembo, R.S. (1978). “Current State of the Art of Algorithms and Computer Software for Geometric Programming,” Jl. Optimization Theory Appl., 26, 149–184.Google Scholar
  7. [7]
    Dinkel, J., Kochenberger, J., and McCarl, B. (1974). “An Approach to the Numerical Solution of Geometric Programming,” Mathematical Programming, 7, 181–190.Google Scholar
  8. [8]
    Duffin, R.J. (1962). “Cost Minimization Problems Treated by Geometric Means,” Operations Res., 10, 668–675.Google Scholar
  9. [9]
    Duffin, R.J. (1970). “Linearizing Geometric Programs,” SIAM Review, 12, 211–227.Google Scholar
  10. [10]
    Duffin, R.J. and Peterson, E.L. (1966). “Duality Theory for Geometric Programming,” SIAM Jl. Appl. Math., 14, 1307–1349.Google Scholar
  11. [11]
    Duffin, R.J., Peterson, E.L., and Zener, C.M. (1967). Geometric Programming, John Wiley, New York.Google Scholar
  12. [12]
    Ecker, J.G. (1980). “Geometric Programming: Methods, Computations, and Applications,” SIAM Review, 22, 338–362.Google Scholar
  13. [13]
    Frank, C.J. (1966). “An Algorithm for Geometric Programming,” in Recent Advances in Optimization Techniques, A. Lavi and T. Vogl, eds., John Wiley, New York, 145–162.Google Scholar
  14. [14]
    Passy, U. and Wilde, D.J. (1967). “Generalized Polynomial Optimizations,” SIAM Jl. Appl. Math., 15, 1344–1356.Google Scholar
  15. [15]
    Peterson, E.L. (1976). “Geometric Programming — A Survey,” SIAM Review, 18, 1–51.Google Scholar
  16. [16]
    Rijckaert, M.J. and Martens, X.M. (1976). “A Condensation Method for Generalized Geometric Programming,” Math. Programming, 11, 89–93.Google Scholar
  17. [17]
    Zener, C. (1961). “A Mathematical Aid in Optimizing Engineering Design,” Proc. Nat. Acad. Sci. U.S.A., 47, 537–539.Google Scholar
  18. [18]
    Zener, C. (1962). “A Further Mathematical Aid in Optimizing Engineering Design,” Ibid., 48, 518–522.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Joseph G. Ecker
    • 1
  1. 1.Rensselaer Polytechnic InstituteTroyUSA