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Computational aspects of cutting-plane algorithms for geometric programming problems

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Abstract

This paper presents the results of computational studies of the properties of cutting plane algorithms as applied to posynomial geometric programs. The four cutting planes studied represent the gradient method of Kelley and an extension to develop tangential cuts; the geometric inequality of Duffin and an extension to generate several cuts at each iteration. As a result of over 200 problem solutions, we will draw conclusions regarding the effectiveness of acceleration procedures, feasible and infeasible starting point, and the effect of the initial bounds on the variables. As a result of these experiments, certain cutting plane methods are seen to be attractive means of solving large scale geometric programs.

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Authors and Affiliations

  1. The Pennsylvania State University, University Park, PA, USA

    John J. Dinkel & Gary A. Kochenberger

  2. Bell Laboratories, Holmdel, NJ, USA

    William H. Elliott

Authors
  1. John J. Dinkel
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  2. William H. Elliott
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  3. Gary A. Kochenberger
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Additional information

This author's research was supported in part by the Center for the Study of Environmental Policy, The Pennsylvania State University.

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Dinkel, J.J., Elliott, W.H. & Kochenberger, G.A. Computational aspects of cutting-plane algorithms for geometric programming problems. Mathematical Programming 13, 200–220 (1977). https://doi.org/10.1007/BF01584337

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  • DOI: https://doi.org/10.1007/BF01584337

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