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On a Compound Duality Classification for Geometric Programming

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Abstract

A classification table for geometric programming is given in this paper. The table is exhaustive and exclusive with only one state in each row and each column. It proves that out of 49 possible duality states, only seven are possible. The proofs of theorems leading to the classification table are based on the new states, which are defined according to the newly defined homogenized programs for both the primal and dual geometric programming.

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Acknowledgements

The authors are indebted to an anonymous referee for many useful comments and suggestions, which helped improve the presentation of the paper.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Northern Michigan University, Marquette, MI, 49855, USA

    Qinghong Zhang

  2. Department of Industrial Engineering, University of Pittsburgh, Benedum Hall, Pittsburgh, PA, 15261, USA

    Kenneth O. Kortanek

Authors
  1. Qinghong Zhang
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  2. Kenneth O. Kortanek
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Correspondence to Qinghong Zhang.

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Zhang, Q., Kortanek, K.O. On a Compound Duality Classification for Geometric Programming. J Optim Theory Appl 180, 711–728 (2019). https://doi.org/10.1007/s10957-018-1415-1

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  • DOI: https://doi.org/10.1007/s10957-018-1415-1

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