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On Duality for a Class of Quasiconcave Multiplicative Programs

Author

Listed:
  • C.H. Scott

    (University of California)

  • T.R. Jefferson

    (Sultan Qaboos University)

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.

Suggested Citation

  • C.H. Scott & T.R. Jefferson, 2003. "On Duality for a Class of Quasiconcave Multiplicative Programs," Journal of Optimization Theory and Applications, Springer, vol. 117(3), pages 575-583, June.
    • Handle: RePEc:spr:joptap:v:117:y:2003:i:3:d:10.1023_a:1023949722269
    DOI: 10.1023/A:1023949722269
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    References listed on IDEAS

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    1. Elmor L. Peterson, 1976. "Fenchel's Duality Thereom in Generalized Geometric Programming," Discussion Papers 252, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Elmor L. Peterson, 1976. "Optimality Conditions in Generalized Geometric Programming," Discussion Papers 221, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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    Cited by:

    1. R. I. Boţ & S. M. Grad & G. Wanka, 2006. "Fenchel-Lagrange Duality Versus Geometric Duality in Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 129(1), pages 33-54, April.

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