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Perfect Duality in Solving Geometric Programming Problems Under Uncertainty

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  • Dennis L. Bricker

    (University of Iowa)

  • K. O. Kortanek

    (University of Iowa)

Abstract

We examine computational solutions to all of the geometric programming problems published in a recent paper in the Journal of Optimization Theory and Applications. We employed three implementations of published algorithms interchangeably to obtain “perfect duality” for all of these problems. Perfect duality is taken to mean that a computed solution of an optimization problem achieves two properties: (1) primal and dual feasibility and (2) equality of primal and dual objective function values, all within the accuracy of the machine employed. Perfect duality was introduced by Duffin (Math Program 4:125–143,1973). When primal and dual objective values differ, we say there is a duality gap.

Suggested Citation

  • Dennis L. Bricker & K. O. Kortanek, 2017. "Perfect Duality in Solving Geometric Programming Problems Under Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 173(3), pages 1055-1065, June.
    • Handle: RePEc:spr:joptap:v:173:y:2017:i:3:d:10.1007_s10957-017-1097-0
    DOI: 10.1007/s10957-017-1097-0
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    References listed on IDEAS

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    2. Rashed Khanjani Shiraz & Madjid Tavana & Debora Di Caprio & Hirofumi Fukuyama, 2016. "Solving Geometric Programming Problems with Normal, Linear and Zigzag Uncertainty Distributions," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 1075-1078, September.
    3. Mandal, Nirmal Kumar & Roy, Tapan Kumar & Maiti, Manoranjan, 2006. "Inventory model of deteriorated items with a constraint: A geometric programming approach," European Journal of Operational Research, Elsevier, vol. 173(1), pages 199-210, August.
    4. Rashed Khanjani Shiraz & Madjid Tavana & Debora Di Caprio & Hirofumi Fukuyama, 2016. "Solving Geometric Programming Problems with Normal, Linear and Zigzag Uncertainty Distributions," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 243-265, July.
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    6. SMEERS, Yves & TYTECA, Daniel, 1984. "A geometric programming model for the optimal design of wastewater treatment plants," LIDAM Reprints CORE 578, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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