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Geometric Programming

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Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 36))

Abstract

The open input–output model with continuous substitution between labor and capital, according to a Cobb–Douglas production function introduced in Section 1.2.8, leads to a mathematical programming problem in which the functions in the constraints are polynomials with positive coefficients (so–called posynomials).

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References and Further Reading

  1. R. Abrams, Optimization models for regional air pollution control, in A. Charnes and W. R. Synn, eds., Mathematical Analysis of Decision Problems in Ecology, Springer-Verlag, Berlin, 1975.

    Google Scholar 

  2. R. G. D. Allen, Macro-Economic Theory: Mathematical Treatment, Macmillan, London, 1968.

    Google Scholar 

  3. K. J. Arrow, H. B. Chenery, B. S. Minhas, and R. M. Solow, Capital-labor substitution and economic efficiency, Rev. Econ. Statist., 43 (1961), 225–250.

    Article  Google Scholar 

  4. V. Balachandran and D. Gensch, Solving the marketing-mix problem using geometric programming, Manage. Sci., 21 (1974), 160–171.

    Article  MATH  Google Scholar 

  5. J. R. Behrman, Sectoral elasticities of substitution between capital and labor in a developing economy: Time series analysis in the case of post-war Chile, Econometrica, 40-2 (1972), 311–326.

    Article  Google Scholar 

  6. Ch. S. Beightler and D. T. Phillips, Applied Geometric Programming,Wiley, NewYork, 1976.

    MATH  Google Scholar 

  7. J. J. Dinkel, G. A. Kochenberger, and Y. Seppala, On the solution of regional planning models via geometric programming, Environ. Planning, 5 (1973), 397–408.

    Article  Google Scholar 

  8. R. J. Duffin, Cost minimization problems treated by geometric means, Oper. Res., 10 (1962), 668–675.

    Article  MATH  MathSciNet  Google Scholar 

  9. R. J. Duffin, E. L. Peterson, and C. Zener, Geometric Programming: Theory and Application, Wiley, NewYork, 1967.

    MATH  Google Scholar 

  10. H. A. Eiselt, G. Pederzoli, and C. L. Sandblom, Continuous Optimization Models, de Gruyter, Berlin, 1987.

    MATH  Google Scholar 

  11. A. S. Kadas, An application of geometric programming to regional economics, Rep. Regional Sci. Assoc., 34 1975), 95–106.

    Google Scholar 

  12. M. Luptáčcik, Geometrische Programmierung und ökonomische Analyse, Mathematical Systems in Economics vol. 32,Verlag Anton Hain, Meisenheim am Glau, Germany, 1977.

    Google Scholar 

  13. A. P. Mastenbroek and P. Nijkamp, A spatial environmental model for an optimal allocation of investments, in P. Nijkamp, ed., Environmental Economics, Vol. 2: Methods, Nijhoff Social Sciences, Leiden, The Netherlands, 1976.

    Google Scholar 

  14. R. E. Miller and P. D. Blair, Input–Output Analysis: Foundations and Extensions, Prentice−Hall, Englewood Cliffs, NJ, 1985.

    MATH  Google Scholar 

  15. B. Nicolleti and L. Mariani, Generalized polynomial programming: Its approach to the solution of some management science problems, Eur. J. Oper. Res., 1 (1977), 239–246.

    Article  Google Scholar 

  16. P. Nijkamp, Planning of Industrial Complexes by Means of Geometric Programming, University Press, Rotterdam, 1972.

    MATH  Google Scholar 

  17. P. Nijkamp and J. H. P. Paelinck, An interregional model of environmental choice, Papers Regional Sci. Assoc., 31 (1977), 51–71.

    Google Scholar 

  18. W. Pinney and J. Modi, An application of geometric programming to the capital budgeting problem, in ORSA Meeting, San Juan, Puerto Rico, ORSA (INFORMS), Hanover, MD, 1974, 46.

    Google Scholar 

  19. A. Rainer, Produktionsfunktionen der österreichischen Industrie, Research Memorandum 88, Institute for Advanced Studies, Vienna, 1974.

    Google Scholar 

  20. M. J. Rijckaert, Engineering applications of geometric programming, in M. Avriel, M. J. Rijckaert, and D. J. Wilde, eds., Optimization and Design, Prentice−Hall, Englewood Cliffs, NJ, 1973.

    Google Scholar 

  21. J. K. Sengupta and J. H. Portillo-Campbell, The approach of geometric programming with economic applications, Z. Staatswirtschaft, 128 (1972), 437–455.

    Google Scholar 

  22. J. Schumann, Input−Output Analyse, Springer-Verlag, Berlin, 1968.

    MATH  Google Scholar 

  23. C. Zener, Mathematical aid in optimizing engineering designs, Proc. Math. Acad. Sci., 47 (1961), 537–539.

    Article  MATH  MathSciNet  Google Scholar 

  24. H. J. Zimmermann, Einführung in die Grundlagen des Operations Research, Verlag Moderne Industrie, Munich, 1971.

    Google Scholar 

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Correspondence to Mikuláš Luptáčik .

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Luptáčik, M. (2010). Geometric Programming. In: Mathematical Optimization and Economic Analysis. Springer Optimization and Its Applications, vol 36. Springer, New York, NY. https://doi.org/10.1007/978-0-387-89552-9_6

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