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On Duality for a Class of Quasiconcave Multiplicative Programs

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Abstract

Multiplicative programs are a difficult class of nonconvex programs that have received increasing attention because of their many applications. However, given their nonconvex nature, few theoretical results are available. In this paper, we study a particular case of these programs which involves the maximization of a quasiconcave function over a linear constraint set. Using results from conjugate function theory and generalized geometric programming, we derive a complete duality theory. The results are further specialized to linear multiplicative programming.

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References

  1. Rosenberg, E., Optimal Module Sizing in VLSI Floor Planning, Zeitschrift fur Operations Research, Vol. 33, pp. 131–143, 1989.

    Google Scholar 

  2. Charnes, A., and Kirby, M., Modular Design, Generalized Inverses, and Convex Programming, Operations Research, Vol. 13, pp. 836–847, 1965.

    Google Scholar 

  3. Kuno, T., and Konno, H., A Parametric Successive Underestimation Method for Convex Multiplicative Programming Problems, Journal of Global Optimization, Vol. 1, pp. 267–285, 1991.

    Google Scholar 

  4. Konno, H., and Kuno, T., Linear Multiplicative Programming, Mathematical Programming, Vol. 56, pp. 51–64, 1992.

    Google Scholar 

  5. Konno, H., and Fukaishi, K., A Branch-and-Bound Algorithm for Solving Low-Rank Linear Multiplicative and Fractional Programming Problems, Journal of Global Optimization, Vol. 18, pp 283–299, 2000.

    Google Scholar 

  6. Liu, X., Umegaki, T., and Yamamoto, Y., Heuristic Methods for Linear Multiplicative Programming, Journal of Global Optimization, Vol. 15, pp. 433–447, 1999.

    Google Scholar 

  7. Ryoo, H., and Sahinidis, N., Analysis of Bounds for Multilinear Functions, Journal of Global Optimization, Vol. 19, pp. 403–427, 2001.

    Google Scholar 

  8. Avriel, M., Diewert, W., Schaible, S., and Zang, I., Generalized Concavity, Plenum Press, New York, NY, p. 162, 1988.

    Google Scholar 

  9. Peterson, E.L., Geometric Programming, SIAM Review, Vol. 18, pp. 1–52, 1976.

    Google Scholar 

  10. Fenchel, W., Convex Cones, Sets, and Functions, Princeton University Press, Princeton, New Jersey, 1953.

    Google Scholar 

  11. Jefferson, T. R., and Scott, C.H., Avenues of Geometric Programming, I: Theory, New Zealand Journal of Operational Research, Vol. 6, pp. 109–136, 1978.

    Google Scholar 

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Authors and Affiliations

  1. Operations and Decision Technologies, Graduate School of Management, University of California, Irvine, California

    C.H. Scott (Professor)

  2. College of Commerce and Economics, Sultan Qaboos University, Oman

    T.R. Jefferson (Professor)

Authors
  1. C.H. Scott
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  2. T.R. Jefferson
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Scott, C., Jefferson, T. On Duality for a Class of Quasiconcave Multiplicative Programs. Journal of Optimization Theory and Applications 117, 575–583 (2003). https://doi.org/10.1023/A:1023949722269

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  • DOI: https://doi.org/10.1023/A:1023949722269

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