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A MILP formulation for generalized geometric programming using piecewise-linear approximations

Author

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  • Tseng, Chung-Li
  • Zhan, Yiduo
  • Zheng, Qipeng P.
  • Kumar, Manish

Abstract

Generalized geometric programming (GGP) problems are converted to mixed-integer linear programming (MILP) problems using piecewise-linear approximations. Our approach is to approximate a multiple-term log-sum function of the form log (x1 + x2 + ⋅⋅⋅ + xn) in terms of a set of linear equalities or inequalities of log x1, log x2, …, and log xn, where x1, …, xn are strictly positive. The advantage of this approach is its simplicity and readiness to implement and solve using commercial MILP solvers. While MILP problems in general are no easier than GGP problems, this approach is justified by the phenomenal progress of computing power of both personal computers and commercial MILP solvers. The limitation of this approach is discussed along with numerical tests.

Suggested Citation

  • Tseng, Chung-Li & Zhan, Yiduo & Zheng, Qipeng P. & Kumar, Manish, 2015. "A MILP formulation for generalized geometric programming using piecewise-linear approximations," European Journal of Operational Research, Elsevier, vol. 245(2), pages 360-370.
    • Handle: RePEc:eee:ejores:v:245:y:2015:i:2:p:360-370
    DOI: 10.1016/j.ejor.2015.01.038
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    References listed on IDEAS

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    1. Han-Lin Li & Hao-Chun Lu, 2009. "Global Optimization for Generalized Geometric Programs with Mixed Free-Sign Variables," Operations Research, INFORMS, vol. 57(3), pages 701-713, June.
    2. Xu, Gongxian, 2014. "Global optimization of signomial geometric programming problems," European Journal of Operational Research, Elsevier, vol. 233(3), pages 500-510.
    3. Tsai, Jung-Fa & Lin, Ming-Hua & Hu, Yi-Chung, 2007. "On generalized geometric programming problems with non-positive variables," European Journal of Operational Research, Elsevier, vol. 178(1), pages 10-19, April.
    4. Qu, Shaojian & Zhang, Kecun & Wang, Fusheng, 2008. "A global optimization using linear relaxation for generalized geometric programming," European Journal of Operational Research, Elsevier, vol. 190(2), pages 345-356, October.
    5. Lin, Ming-Hua & Tsai, Jung-Fa, 2012. "Range reduction techniques for improving computational efficiency in global optimization of signomial geometric programming problems," European Journal of Operational Research, Elsevier, vol. 216(1), pages 17-25.
    6. Peiping Shen & Xiaoai Li, 2013. "Branch-reduction-bound algorithm for generalized geometric programming," Journal of Global Optimization, Springer, vol. 56(3), pages 1123-1142, July.
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    Cited by:

    1. Yiduo Zhan & Qipeng P. Zheng & Chung-Li Tseng & Eduardo L. Pasiliao, 2018. "An accelerated extended cutting plane approach with piecewise linear approximations for signomial geometric programming," Journal of Global Optimization, Springer, vol. 70(3), pages 579-599, March.
    2. Shen, Peiping & Zhu, Zeyi & Chen, Xiao, 2019. "A practicable contraction approach for the sum of the generalized polynomial ratios problem," European Journal of Operational Research, Elsevier, vol. 278(1), pages 36-48.

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