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A global optimization using linear relaxation for generalized geometric programming

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  • Qu, Shaojian
  • Zhang, Kecun
  • Wang, Fusheng

Abstract

Many local optimal solution methods have been developed for solving generalized geometric programming (GGP). But up to now, less work has been devoted to solving global optimization of (GGP) problem due to the inherent difficulty. This paper considers the global minimum of (GGP) problems. By utilizing an exponential variable transformation and the inherent property of the exponential function and some other techniques the initial nonlinear and nonconvex (GGP) problem is reduced to a sequence of linear programming problems. The proposed algorithm is proven that it is convergent to the global minimum through the solutions of a series of linear programming problems. Test results indicate that the proposed algorithm is extremely robust and can be used successfully to solve the global minimum of (GGP) on a microcomputer.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:190:y:2008:i:2:p:345-356
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    Cited by:

    1. Xing, Li-Ning & Chen, Ying-Wu & Yang, Ke-Wei, 2009. "A novel mutation operator based on the immunity operation," European Journal of Operational Research, Elsevier, vol. 197(2), pages 830-833, September.
    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.
    3. 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.
    4. Peiping Shen & Yuan Ma & Yongqiang Chen, 2011. "Global optimization for the generalized polynomial sum of ratios problem," Journal of Global Optimization, Springer, vol. 50(3), pages 439-455, July.
    5. 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.
    6. Ying Ji & Mark Goh & Robert Souza, 2016. "Proximal Point Algorithms for Multi-criteria Optimization with the Difference of Convex Objective Functions," Journal of Optimization Theory and Applications, Springer, vol. 169(1), pages 280-289, April.

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