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Geometrisches Optimieren — eine Übersicht

Übersichtsvortrag
  • O. Krafft
Conference paper
Part of the Proceedings in Operations Research book series (ORP, volume 1973)

Summary

This is a (non-exhaustive) survey on the theory of geometric programming. In the first part the prototype geometric program is presented together with its dual. The second part deals with recent trends in the development of the theory, namely imbedding the theory in more general theories and generalizations of the theory toward a setting with a wider spectrum of applications (algebraic geometric programming).

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Literatur

  1. [1]
    R. J. Duffin, E. L. Peterson, C. Zener: Geometric Programming-Theory and Application, John Wiley, New York, 1967.Google Scholar
  2. [2]
    M.Avriel: Fundamentals of geometric programming, Proc.NATO Conf. on Appl. of Math.Programming, E.M.L.Beale, ed.Google Scholar
  3. [3]
    M. Avrie1, A. C. Williams: Complementary geometric programming, SIAM J. App1.Math. 19 (1970), 125–141.CrossRefGoogle Scholar
  4. [4]
    E. F. Beckenbach, R. Bellman: Inequalities, Springer, Berlin 1965.Google Scholar
  5. [5]
    R. J. Duffin: Linearizing geometric programs, SIAM Review 12 (1970).Google Scholar
  6. [6]
    R. J. Duffin, E. L. Peterson: Reversed geometric programs treated by harmonic means, Ind.Univ.Math Journ. 22 (1972), 531–550.CrossRefGoogle Scholar
  7. [7]
    R. J. Duffin, E. L. Peterson: The proximity of (algebraic) geometric programming to linear programming, Math.Programming 3 (1972), 250–253CrossRefGoogle Scholar
  8. [8]
    R. J. Duffin, E. L. Peterson: Geometric programs treated with slack variables, Applicable Analysis 2 (1972), 255–267.CrossRefGoogle Scholar
  9. [9]
    R. J. Duffin, E. L. Peterson: Geometric programming with signomia1s, Journ.Opt.Theory and Appl. 11 (1973), 3–35.CrossRefGoogle Scholar
  10. [10]
    M. Hamala: Geometric programming in terms of conjugate functions, CORE Discussion paper no. 6811, (1968).Google Scholar
  11. [11]
    G. H. Hardy, J. E. Littlewood, G. Polya: Inequalities, Cambridge University Press, Cambridge, 1959.Google Scholar
  12. [12]
    J. Hartung: Dua1ität und Sattelpunkte, Op.Res.Verfahren 12 (1971), 194–200.Google Scholar
  13. [13]
    G. A. Kochenberger, R. E. D. Woolsey, B. A. McCarl: On the solution of geometric programs via separable programming, Op.Res.Quart. 24 (1973), 285–294.CrossRefGoogle Scholar
  14. [14]
    O. Krafft: Geometric programming as a special case of Dieter’s optimality theory, Op.Res.Verfahren 8 (1969), 121–128.Google Scholar
  15. [15]
    O. Krafft: Programming methods in statistics and probability theory, in: Nonlinear Programming; Rosen., Mangasarian, Ritter, eds., Academic Press, New York, 1970, 425–446.Google Scholar
  16. [16]
    A. J. Morris: Approximation and complementary geometric programing, SIAM J. Appl. Math. 23 (1972), 527–531.CrossRefGoogle Scholar
  17. [17]
    L. D. Pascual, A. Ben-Israel: Constrained maximization of posynomia1s by geometric programming, Jour.Opt.Th.Appls. 5 (1970),73–80.CrossRefGoogle Scholar
  18. [18]
    L. D. Pascual, A. Ben-Israel: Vector-valued criteria in geometric programming, Op.Res. 19 (1971), 98–104.CrossRefGoogle Scholar
  19. [19]
    U. Passy: Nonlinear assignment problems treated by geometric programming, Op.Res. 19 (1971),1675–1690.CrossRefGoogle Scholar
  20. [20]
    R. T. Rockafellar: Some convex programs whose duals are linearly contrained, in: Nonlinear Programming; Rosen, Mangasarian, Ritter, eds., Academic Press, New York, 1970, 293–322.Google Scholar
  21. [21]
    H. Theil: Substitution effects in geometric programming, Man.Sci. 19 (1972), 25–30.Google Scholar
  22. [22]
    B.L.van der Waerden: “Aufgabe 45”, Jahresber. Deutsche Math.Verein. 35 (1926), S. 117.Google Scholar
  23. [23]
    W. Vogel: Dualitatsaussagen fur nichtkonvexe Optimierungsaufgaben, Op.Res.Verfahren 13 (1971),394–415.Google Scholar
  24. [24]
    D. J. Wilde, C. S. Beightler: Foundations of Optimization, Prentice Hall, Englewood Cliffs, 1967, pp. 99–133.Google Scholar
  25. [25]
    W. I. Zangwill: Nonlinear Programming, Prentice Hall, Englewood Cliffs, 1969, 68–76.Google Scholar

Copyright information

© Physica-Verlag, Rudolf Liebing KG, Würzburg 1974

Authors and Affiliations

  • O. Krafft
    • 1
  1. 1.HamburgDeutschland

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